How to add rational expressions.

Answers

Answer 1
First, some general rules to remember:

Rational expressions (fractions) can only be added or subtracted if they have a common denominator.
The numerator and denominator of a fraction may be multiplied by the same quantity. This will result in a fraction that is equivalent to the original fraction.
For a fractional answer to be in final form, the fraction must be reduced to lowest terms.
Adding or subtracting rational expressions is a four-step process:

Write all fractions as equivalent fractions with a common denominator.
Combine the fractions as a single fraction that has the common denominator.
Simplify the expression in the top of the fraction.
Reduce the fraction to lowest terms.
To see this process, we'll look at some examples.


Example 1

Step 1: To find a common denominator, start by factoring the denominators of both fractions.



The least common denominator of these two fractions is 2(x+6)(x-6).

Looking at the first fraction, we can see that the factor missing from its denominator is (x-6). In the next step, we'll multiply the top and bottom of the first fraction by (x-6).

Looking at the second fraction, we can see that the factor missing from its denominator is 2. In the next step, we'll multiply the top and bottom of the second fraction by 2.






Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:






Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.



Step 4: Now we'll reduce the fraction to lowest terms










Example 2



Step 1: To find a common denominator, start by factoring the denominators of both fractions.



The least common denominator of these two fractions is (x+4)(x+1)(x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+3). In the next step, we'll multiply the top and bottom of the first fraction by (x+3).

Looking at the first fraction, we can see that the factor missing from its denominator is (x+4). In the next step, we'll multiply the top and bottom of the first fraction by (x+4).






Step 2: Now that the fractions have the same denominators, we'll create one combined fraction by adding the two fractions together:






Step 3: We'll simplify the top of the fraction. Notice that we are only simplifying the top of the fraction; the bottom of the fraction remains unchanged.










Step 4: Now we'll reduce the fraction to lowest terms


Related Questions

what's y'all's favorite netflix movie ?

Answers

Answer:7 deadly sins cursed by light

Step-by-step explanation:

The lines represented by the equations 5y - x = 5 and y - x = 1 are

Answers

Answer:

Same line

Step-by-step explanation:

5y - x = 5                           y - 1/5x = 1

5y = x + 5                           y = 1/5x + 1

5y/5 = x/5 + 5/5

 y =  1/5x + 1

factorize 21xy - 14xz - 28wx

Answers

Answer:

7x(3y - 2z - 4w)

Step-by-step explanation:

21xy - 14xz - 28wx ← factor out 7x from each term

= 7x(3y - 2z - 4w)

Answer:

7 x . (3y - 2z - 4w

Step-by-step explanation:

There is a line that includes the point (5, -7) and has a slope of -1. What is its equation in slope-intercept form?

Answers

y + 7 = -1(x - 5)

y + 7 = -x + 5

y = -x - 2

someone
someone
someone
somone

Answers

Answer:

-24

Step-by-step explanation:

have a great day! feel free to mark as brainliest! :)

Which inequality is represented by the graph?

Answers

Answer:

y <  -3/2x + 1

Step-by-step explanation:

Points (-2,4) and (2, -2) are on the graph.

The graph crosses the y-axis at 1 so the y-intercept is 1

Slope = (change in the y-value)/(change in the x-value.

Slope = (-2 - 4)/ [2 - (- 2)]

Slope = -6/4

Slope = -3/2  

The equation of the line : y = -3/2x + 1

Now the graph is dotted and it is shaded down.

Therefore the inequality is y <  -3/2x + 1

The value of a new car in 2015 was 40,000 dollar. It depreciates each year by 7%. How much will the car be worth in 2026?

Answers

Answer:

9200 dollars

Step-by-step explanation:

just minus it 77%

Explain what the point (6,2) represents.

Answers

Answer:  6 is the 1st term, 2 is the common ratio

Step-by-step explanation: T = 6(2d-1)


What number does this Roman numeral represent?
XXXII

Answers

Answer: 32

Step-by-step explanation:

The roman numeral XXXII is 32 and XXIII is 23.

The number for this Roman numeral XXXII is, 32

Given that,

We have to write the number for this Roman numeral  XXXII.

Since, We know that,

X represent in number = 10

I represent in number = 1

Hence, The number for this Roman numeral  XXXII is,

⇒ XXXII

⇒ (10 + 10 + 10 + 1 + 1)

⇒ 32

Therefore, the number for this Roman numeral  XXXII is, 32

Learn more about Number system visit:

https://brainly.com/question/17200227

#SPJ6

Each year, the students in seventh grade go to an environmental camp. This year, the total cost is $1,580 for 79 students. Which equation represents the cost, y, of attending the camp for x number of students?

Select the correct answer.
y = 20x
y = 79x
y = 79x + 1580
y = 1580x + 79

Answers

y=79x+1580, this is the correct answer

Answer:

y=20x

Step-by-step explanation:

You have to find the cost by dividing the amount of money by the amount of students, to see house much each student paid. You are finding the unit price. Which is 20 because...

1.580/79=20

In conclusion,

Each student paid $20

I need help please brainliest to correct answer
NO BOTSSSS PLEASEEEE
Also if you want fr33 p0!ints go answer my last question

Why are various creative works split up into different types under copyright law?


Some artists look for ways to extend copyright for longer than the laws normally allow. Why do they do this?


What kinds of artists benefit the most from creative commons licenses? Explain your answer.


Why is it useful for students to practice the MLA and APA citation methods?


What kinds of art works can be considered remixes or mashups? Explain your answer.

Answers

Answer:

1. The nature of creative work is that it can take almost any form, so the scope of the copyright law was drafted in such a way to take that into account. The categories that works can potentially be protected in are so wide that it’s difficult to imagine what types of creative work are not protected.

2.Some artists look for ways to extend copyright for longer than the laws normally allow. Why do they do this?

3.The Benefits of Using a Creative Commons License Numerous high-profile authors (including futurist Cory Doctorow), artists, musicians (such as the rock band Nine Inch Nails), and even government agencies and entities (including the White House) use Creative Commons licenses. You’ll find many more case studies on the Creative Commons site.

Step-by-step explanation:

Answer:

What kinds of artists benefit the most from creative commons licenses? Explain your answer.

Every license helps creators, they are called licensors if they use our tools  retain copyright while allowing others to copy, distribute, and make some uses of their work  at least non-commercially. Every Creative Commons license also ensures licensors get the credit for their work they deserve.

the number of fish in a lake decreasing by 400 every year,as described by the function below. f(1)=8200 f(n+1)=f(n)-400 what will be the value

Answers

The number of fish in the lake is an illustration of arithmetic sequence

The value of f(2) is 7800, and it represents the number of fish in the lake, the second year

The model is given as:

[tex]\mathbf{f(n+1) = f(n) - 400}[/tex]

Where [tex]\mathbf{f(1) = 8200}[/tex]

To calculate f(2), we simply take n as 1.

i.e. n = 1

Substitute 1 for n in [tex]\mathbf{f(n+1) = f(n) - 400}[/tex]

So, we have:

[tex]\mathbf{f(1+1) = f(1) - 400}[/tex]

Add 1 and 1

[tex]\mathbf{f(2) = f(1) - 400}[/tex]

Substitute 8200 for f(1)

[tex]\mathbf{f(2) = 8200 - 400}[/tex]

Subtract

[tex]\mathbf{f(2) = 7800}[/tex]

Hence, the value of f(2) is 7800

Read more about sequence at:

https://brainly.com/question/18109692

I need help plz it’s for school plz plz

Answers

Answer:

y = 3x + 1

Step-by-step explanation:

CAN SOMEONE HELP ME PLEASE ASAP!

Answers

The answer is P and R

Answer:

Q and R

Step-by-step explanation:

to be similar all sides must have the same scaling factor :

the factor from 2 to 8 is 4.

and the factor from 3 to 12 is also 4.

therefore, these 2 parallelograms are similar.

Justine and Kate are training for a race.
At every training session Justine runs x miles and Kate runs 3 more miles than Justine.
In one week, Justine and Kate both train every day.
In the 7 days they run 63 miles in total between them.
How many miles do Justine and Kate each run per day?

Answers

Answer:

Justine runs 3 miles a day and Kate runs 6 miles a day.

Step-by-step explanation:

x = number of miles ran in a day

x(7) + (x+3)(7) = 63

7x + 7x + 21 = 63

14x + 21 = 63

14x = 42

x = 3

3 + 3 = 6

Justine runs 3 miles a day and Kate runs 6 miles a day.

Will give brainliest!

Answers

Answer:

1[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

17/20 + 7/20

17+7=24

24/20 =1.2

1 [tex]\frac{4}{20}[/tex]

can simplify to be 1[tex]\frac{1}{5}[/tex]

Answer:

1 1/5

Step-by-step explanation:

17/20 + 7/20 is equal to 24/20. Because the denominater (20 in this case) is the same we can leave it there and just add the numerator.

Now to simplify into a proper fraction. We know that only 1, 20 goes into 24 because if there was 2, 20's it would be 40 which is greater than 24. So 24 - 20 is 4. Therefore the answer is 1 4/20 which can be simplified to 1 1/5

please answer and show work ill give u 70 point

Answers

1.answer

15/8-5/8=10/8answer

2.

9/5-1/5=8/5answer

3.3/2-1/2=2/2answer

Answer:

first question= 7/8

second question= 8/5

third question= 1

fourth question=23/8

fifth question=9/8

final question= 1/3

Step-by-step explanation:

1) 15/8 - 5/8 = 7/8

since the denominator is the same, it will be easier

do 15-8

which is 7

so the final answer is 7/8

(Remember that you don't subtract the denominator)

2) 9/5 - 1/5 = 8/5

Using the same method as the first question, you should get 8/5

8/5 as a mixed fraction would be 1 3/5

3) 1 1/2 - 1/2= 1

1 1/2 into a mixed fraction = 3/2

3/2-1/2

=2/2, which is 1

4) 3 1/4 - 3/8=23/8

3 1/4 as a mixed fraction is 13/4

so the equation would be 13/4 - 3/8

however, the denominator is not the same

and the least common multiple is 8

so 13/4 = 26/8

26/8-3/8= 23/8

5) 5/4 - 1/8 = 9/8

5/4 doesn't have the same denominator as 1/8, so you change it into 10/8

10/8-1/8

9/8

6) final question :)

5/6 - 1/2= 1/3

1/2 = 3/6

5/6-3/6

=2/6

after simplifying= 1/3

Hope it helps and have a nice day!

Mark me as branliest pls

can you guys help me

5x3+7=50? this is g.e.m.d.a.s

Answers

Answer:

It's 27

Step-by-step explanation:

5x3 = 15 + 7 =27

If Kevin has 3/4 of a rope in needs 4/8 of a rope how much more rope does he need.

Answers

If he needs 4/8 then he doesn't need anymore rope because 3/4 is equal to 6/8

11. In right triangle CAT, angle. If CA = 6 and CT = 8, find AT.

Answers

Answer:

AT=5.29 or 2√7

Step-by-step explanation:

Pythagorean  theory

a²+b²=c²

CAT means ∡ A is 90°

so CA is one of the leg (a) and AT the other leg (b)

CT is the (c)

6²+b²=8²

b²=64-36

b=√28

=5.29

someone please help me asap

Answers

Answer:

I only can see that one of them are B i don't know for the rest

Step-by-step explanation:

what is the formula for calculating midpoint​

Answers

MIDPOINT

The intersection of a line segment's two endpoints is known as the midpoint. From the midpoint to one endpoint and the midpoint to the other endpoint, you will be given two equal distances.

The formula for calculating the midpoint is given below:

[tex] \boxed{ \bold{ \: \: M = \bigg(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\bigg) \: \: }}[/tex]

For example, let us try solving this sample problem below using the midpoint formula:

Sample problem: A new transmission tower will be put up midway between two existing towers. On a map drawn on a coordinate plane, the coordinates of first existing tower are (-5, -3) and the coordinates of the second existing tower are (9, 13). What are the coordinates of the point where the new tower will be placed?

From inspection on the given problem:

[tex]\sf (x_1, y_1) = (-5, -3) [/tex][tex]\sf (x_2, y_2) = (9, 13) [/tex]

Substitute the given values into the midpoint formula and solve for M:

[tex]\sf M = \bigg(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\bigg)[/tex]

[tex]\sf M = \bigg(\dfrac{-5 + 9}{2}, \dfrac{-3 + 13}{2}\bigg)[/tex]

[tex]\sf M = \bigg(\dfrac{4}{2}, \dfrac{10}{2}\bigg)[/tex]

[tex]\sf M = (2, 5)[/tex]

Therefore, the coordinates of the point are (2, 5).

[tex]\\[/tex]

Now, wasn't that easy? Try this other sample problem:

The endpoints of a segment are (-5, 2) and (9, 12), respectively. What are the coordinates of its midpoint?

From the sample problem above, you may solve it on your own to enhance your skill on calculating the midpoint.

Cheers!

Will the value of each power will be + or - ?
4. (-64
5. (-3)?

Plzzz help

Answers

Answer:

4. Positive (+)

5. Negative (-)

Step-by-step explanation:

When the exponent is even, the value will be positive (+). If the exponent it's odd, the value will be negative (-). This only applies when the number in the parenthesis is a negative number.

4) Solution:

→ (-6)⁴

→ -6 × -6 × -6 × -6

→ +1296

Ans: Positive

5) Solution:

→ (-3)⁷

→ -3 × -3 × -3 × -3 × -3 × -3 × -3

→ -2187

Ans: Negative

GEOMETRY QUESTION W PICTURE

Answers

Answer:

R

Step-by-step explanation:

E is congruent to R because of angle stuff

Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?

Answers

Step-by-step explanation:

Given:

Lemons - l and apples - aa = 35¢, l = 15¢Number of apples and lemons = 17Cost of lemons and apples = $3.95 = 395¢

System as per question:

a + l = 1735a + 15l = 395

Or

a + l = 170.35a + 0.15l = 3.95

Step-by-step explanation:

Let the number of apples be a and lemons be l . Then ,

=> a + l = 17

Also ,

=> 35a + 15l = $ 3.95

What bed level deviation is considered precise.

Answers

Answer: A levelling map viewed in Optoprint shows a 0.7mm deviation 'high' in the rear right corner vs the front left 'home' position of the bed.

Step-by-step explanation:

I need help fast please

About 8% of canada is covered in fresh water
the area of canada is approximately 9,970,000km
a calculate the area covered in fresh water
b how much of canada is not covered in fresh water
23%of canada is covered in tundra estamaite tundra covered area

thanks ​

Answers

Answer:

797600km, 9172400 km, 2293100 km

Step-by-step explanation:

a. to find the amount of canada covered in fresh water, multiply 9970000 by 0.08 to get 797600km

b. the amount not covered by fresh water is 9970000-797600 which equals 9172400 km

c. multiply area of canada by 0.23 which is 2293100 km

just in case you might want to double check the zeros to make sure i did it right

Answer:

a. 797,600 km²

b. 9,172,400 km²

c. 2,293,100 km²

Step-by-step explanation:

To find a percent of a number, multiply the percent by the number. First, change the percent into a decimal number by moving the decimal point of the percent 2 places to the left. For example, 42% = 0.42; 7% = 0.07

Part a.

8% of 9,970,000 km²

Step 1. Multiply the percent by the number

8% of 9,970,000 km² = 8% × 9,970,000 km²

Step 2. Change the percent into a decimal number by moving the decimal point of the percent 2 places left.

8% of 9,970,000 km² = 8% × 9,970,000 km² = 0.08 × 9,970,000 km²

Step 3. Use a calculator or long division to do the multiplication.

0.08 × 9,970,000 km² = 797,600 km²

Answer: a. area covered in fresh water is 797,600 km²

Part b.

Subtract the area of part a. from the total area of Canada.

9,970,000 km² - 797,600 km² = 9,172,400 km²

Answer: b. area not covered in fresh water is 9,172,400 km²

Part c.

Tundra is 23% of total area.

23% of 9,970,000 km²

Step 1. Multiply the percent by the number

23% of 9,970,000 km² = 23% × 9,970,000 km²

Step 2. Change the percent into a decimal number by moving the decimal point of the percent 2 places left.

23% of 9,970,000 km² = 23% × 9,970,000 km² = 0.23 × 9,970,000 km²

Step 3. Use a calculator or long division to do the multiplication.

0.23 × 9,970,000 km² = 2,293,100 km²

Answer: a. area covered in tundra is 2,293,100 km²

80 POINTS!!! HELP ASAP!!!!

Select the correct answer.
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g.

g(x) = f(x − 3) + 4

A.
The graph of function f is shifted right 3 units and down 4 units.
B.
The graph of function f is shifted right 3 units and up 4 units.
C.
The graph of function f is shifted left 3 units and down 4 units.
D.
The graph of function f is shifted left 3 units and up 4 units.

Answers

Answer:

its c

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation: shifted right 3 units and up 4 units.

Jessica is a custodian at Oracle Arena. She waxes 20 square meters of the floor in 3/5 of an hour. She waxes the floor at a constant rate.

At this rate, how many square meters can she wax per hour?

Answers

divide 20 by 3 to see how much she would wax in 1/5 of an hour.
20/3= 6.66666667
6.66666667 * 5 =
33.3333333
i think :)

a garden snail moves 1/6 foot in 1/3 hours. Find the speed of the snail in feet per hour

Answers

(1/6)/(1/3)
1/6 x 3/1
1/6 x 3
3/6
1/2

3/6 = 1/2 fph = .5fph

Other Questions
The following question references the novel Mrs. Dalloway by Virginia WoolfInferences are conclusions drawn from either evidence or reasoning presented in a novel. What are some of the inferencesmade regarding Septimus Smith and his condition? Describe his symptoms, the cause of his condition, how it affects hislife and how it affects his wife Lucrezia. Help for brainliest:)Variation in offspring is important in maintaining genetic diversity within a population . Which of the answer choices indicates a mechanism of introducing genetic variation in a population? Select all that apply. A crossing over during meiosis B ) fertilization of an egg by a sperm C) independent assortment during meiosis D) mitosis producing two new daughter cells E) binary fission resulting in two bacterial daughter cells The Industrial RevolutionSelect one:a. resulted in an end to colonialism.b. required the greater use of energy.c. had little effect on agriculture. Emilio's family is going on vacation. His mom and sister leave at7:00 in the morning, driving an average of 45 miles per hour.Emilio and his dad leave at 8:00. His dad drives an average of60 miles per hour.Will Emilio and his dad catch up to his mom and sister? I'll give brainliest and extra points if someone helps me with all the questions!! Read the authors Notice from The Adventures of Huckleberry Finn and answer the question.Persons attempting to find a motive in this narrative will be prosecuted; persons attempting to find a moral in it will be banished; persons attempting to find a plot in it will be shot.What is the authors purpose in including this ironic notice?A. to remind readers that The Adventures of Huckleberry Finn has no political agendaB. The Adventures of Huckleberry Finn is intended to be read rather than analyzed.C. The Adventures of Huckleberry Finn is meant to be a serious work of literature.D. to warn readers that The Adventures of Huckleberry Finn does not follow a typical plot*D is wrong* taughttaught /tt/verbpast tense of teach, meaning to show or explain how to do somethingtauttaut /tt/adj.pulled tightpourspours /prs/verbmoves in a continuous flowporespores /prs/verbstudies intentlyThe students were __________ that an accomplished scientist always _____ over the results of an experiment. Which homophones correctly complete the sentence?taught, pourstaught, porestaut, pourstaut, pores How many students read in 15 minutes between 8am and 9am Work out the percentage change when a price of 40 is decreased to 18 The right whale is an example of A. a species that is recovering from being endangered B. a species that failed to adapt to changes to its environment C. a species that is almost gone because of the excessive pollution in its habitat D. a species that has become too populous and threatens the survival other of species Please Help Me Solve This! I Need Help Now!Correct Answer = Brainliest A force of 6.0 N acts on a 4.0 Kg object for 10.0s. What is the object's change in momentum? What economic policy did Secretary of the Treasury Andrew Mellon favor? A breaking up monopolies and protecting the rights of workers B restricting the absolute freedom of business leaders C advancing business interests and lowering taxesD lowering tariff rates on foreign imports Beethoven wrote his Symphony No. 9 when he was completely deaf. Losing his hearing caused him much sadness and anger. What differences in his music can you hear between Symphony No. 5 and Symphony No. 9? ----------------------------- help me with this please!?!?!?!?! qu caractersticas tienen los personajes principales de un cuento Can someone please explain this to me please? Will give brainly if you actually answer the question If customer satisfaction does not always lead to customer loyalty, firms may need to focus additional effort on _____ strategies.. True / False: ANOVA, Part I. Determine if the following statements are true or false in ANOVA, and explain your reasoning for statements you identify as false.(a) As the number of groups increases, the modified significance level for pairwise tests increases as well.(b) As the total sample size increases, the degrees of freedom for the residuals increases as well.(c) The constant variance condition can be somewhat relaxed when the sample sizes are relatively consistent across groups.(d) The independence assumption can be relaxed when the total sample size is large.