Adding and Subtracting Rational Expressions

Question 1

Add 2/(x + 3) + 4/(x - 3) and write the result with the denominator in factored form.

Accepted Answer

(6x + 6)/((x + 3)(x - 3))

Answer

(6x - 6)/((x + 3)(x - 3))

Answer

(6x + 18)/((x + 3)(x - 3))

Answer

6/((x + 3)(x - 3))

Question 2

Add 4/(x - 1) + 7/(x + 1) and write the result with the denominator in factored form.

Accepted Answer

(11x - 3)/((x - 1)(x + 1))

Answer

(11x + 3)/((x - 1)(x + 1))

Answer

(11x - 11)/((x - 1)(x + 1))

Answer

11/((x - 1)(x + 1))

Question 3

Add 5/(x^2 - x - 2) + 4/(x + 1) and write the result with the denominator in factored form.

Accepted Answer

(4x - 3)/((x + 1)(x - 2))

Answer

(4x - 8)/((x + 1)(x - 2))

Answer

9/((x + 1)(x - 2))

Answer

(4x - 3)/((x + 1)(x - 2)^2)

Question 4

Add 6/(x - 5) + 5/(x + 1) and write the result with the denominator in factored form.

Accepted Answer

(11x - 19)/((x - 5)(x + 1))

Answer

(11x + 19)/((x - 5)(x + 1))

Answer

(11x - 31)/((x - 5)(x + 1))

Answer

11/((x - 5)(x + 1))

Question 5

Add 6/(x^2 - 7x + 12) + 4/(x - 3) and write the result with the denominator in factored form.

Accepted Answer

(4x - 10)/((x - 3)(x - 4))

Answer

(4x - 16)/((x - 3)(x - 4))

Answer

10/((x - 3)(x - 4))

Answer

(4x - 10)/((x - 3)(x - 4)^2)

Question 6

What is the least common denominator of 3/(x^2 - 9) and 5/(x^2 + 6x + 9)?

Accepted Answer

(x - 3)(x + 3)^2

Answer

(x - 3)(x + 3)

Answer

(x + 3)^2

Answer

(x^2 - 9)(x^2 + 6x + 9)

Question 7

Subtract 4/(x - 5) - 2/(x - 2) and write the result with the denominator in factored form.

Accepted Answer

(2x + 2)/((x - 5)(x - 2))

Answer

(2x - 18)/((x - 5)(x - 2))

Answer

(6x - 18)/((x - 5)(x - 2))

Answer

(6x + 2)/((x - 5)(x - 2))

Question 8

Subtract 6/(x + 2) - 2/(x - 2) and write the result with the denominator in factored form.

Accepted Answer

(4x - 16)/((x + 2)(x - 2))

Answer

(4x - 8)/((x + 2)(x - 2))

Answer

(8x - 8)/((x + 2)(x - 2))

Answer

(8x - 16)/((x + 2)(x - 2))

Question 9

Add 8/(x^2 - 7x + 6) + 3/(x - 6) and write the result with the denominator in factored form.

Accepted Answer

(3x + 5)/((x - 6)(x - 1))

Answer

(3x - 3)/((x - 6)(x - 1))

Answer

11/((x - 6)(x - 1))

Answer

(3x + 5)/((x - 6)(x - 1)^2)

Question 10

A student writes 4/(x + 1) + 7/(x - 2) = 11/(2x - 1). What did the student do wrong?

Accepted Answer

added the denominators instead of rewriting both terms over a common denominator

Answer

used a common denominator that was not the least one

Answer

forgot to distribute a negative sign

Answer

canceled a factor that was not common to both terms

Question 11

Subtract 7/(x + 2) - 2/(x + 1) and write the result with the denominator in factored form.

Accepted Answer

(5x + 3)/((x + 2)(x + 1))

Answer

(5x + 11)/((x + 2)(x + 1))

Answer

(9x + 11)/((x + 2)(x + 1))

Answer

(9x + 3)/((x + 2)(x + 1))

Question 12

Add 5/(x - 5) + 4/(x - 4) and write the result with the denominator in factored form.

Accepted Answer

(9x - 40)/((x - 5)(x - 4))

Answer

(9x + 40)/((x - 5)(x - 4))

Answer

(9x)/((x - 5)(x - 4))

Answer

9/((x - 5)(x - 4))

Question 13

Subtract 6/(x - 3) - 3/(x + 4) and write the result with the denominator in factored form.

Accepted Answer

(3x + 33)/((x - 3)(x + 4))

Answer

(3x + 15)/((x - 3)(x + 4))

Answer

(9x + 15)/((x - 3)(x + 4))

Answer

(9x + 33)/((x - 3)(x + 4))

Question 14

Subtract 7/(x + 3) - 3/(x + 4) and write the result with the denominator in factored form.

Accepted Answer

(4x + 19)/((x + 3)(x + 4))

Answer

(4x + 37)/((x + 3)(x + 4))

Answer

(10x + 37)/((x + 3)(x + 4))

Answer

(10x + 19)/((x + 3)(x + 4))

Question 15

Subtract 6/(x + 1) - 5/(x + 4) and write the result with the denominator in factored form.

Accepted Answer

(x + 19)/((x + 1)(x + 4))

Answer

(x + 29)/((x + 1)(x + 4))

Answer

(11x + 29)/((x + 1)(x + 4))

Answer

(11x + 19)/((x + 1)(x + 4))

Question 16

What is the least common denominator of 4/(x^2 - 36) and 9/(x^2 + 12x + 36)?

Accepted Answer

(x - 6)(x + 6)^2

Answer

(x - 6)(x + 6)

Answer

(x + 6)^2

Answer

(x^2 - 36)(x^2 + 12x + 36)

Question 17

What is the least common denominator of 2/(x^2 - 4) and 7/(x^2 - 4x + 4)?

Accepted Answer

(x + 2)(x - 2)^2

Answer

(x + 2)(x - 2)

Answer

(x - 2)^2

Answer

(x^2 - 4)(x^2 - 4x + 4)

Question 18

What is the least common denominator of 4/(x^2 - 4) and 9/(x^2 + 5x + 6)?

Accepted Answer

(x - 2)(x + 2)(x + 3)

Answer

(x + 2)

Answer

(x - 2)(x + 3)

Answer

(x^2 - 4)(x^2 + 5x + 6)

Question 19

Add 4/(x - 1) + 5/(x - 4) and write the result with the denominator in factored form.

Accepted Answer

(9x - 21)/((x - 1)(x - 4))

Answer

(9x + 21)/((x - 1)(x - 4))

Answer

(9x + 11)/((x - 1)(x - 4))

Answer

9/((x - 1)(x - 4))

Question 20

Add 5/(x^2 + 8x + 15) + 3/(x + 3) and write the result with the denominator in factored form.

Accepted Answer

(3x + 20)/((x + 3)(x + 5))

Answer

(3x + 15)/((x + 3)(x + 5))

Answer

8/((x + 3)(x + 5))

Answer

(3x + 20)/((x + 3)(x + 5)^2)

Question 21

Subtract 3/(x - 1) - 2/(x + 1) and write the result with the denominator in factored form.

Accepted Answer

(x + 5)/((x - 1)(x + 1))

Answer

(x + 1)/((x - 1)(x + 1))

Answer

(5x + 1)/((x - 1)(x + 1))

Answer

(5x + 5)/((x - 1)(x + 1))

Question 22

A student writes 4/(x + 1) + 3/(x - 3) = 7/(2x - 2). What did the student do wrong?

Accepted Answer

added the denominators instead of rewriting both terms over a common denominator

Answer

used a common denominator that was not the least one

Answer

forgot to distribute a negative sign

Answer

canceled a factor that was not common to both terms

Question 23

Subtract 5/(x + 5) - 3/(x + 4) and write the result with the denominator in factored form.

Accepted Answer

(2x + 5)/((x + 5)(x + 4))

Answer

(2x + 35)/((x + 5)(x + 4))

Answer

(8x + 35)/((x + 5)(x + 4))

Answer

(8x + 5)/((x + 5)(x + 4))

Question 24

A student writes 3/(x + 1) + 3/(x - 3) = 6/(2x - 2). What did the student do wrong?

Accepted Answer

added the denominators instead of rewriting both terms over a common denominator

Answer

used a common denominator that was not the least one

Answer

forgot to distribute a negative sign

Answer

canceled a factor that was not common to both terms

Question 25

Add 2/(x^2 + 9x + 18) + 4/(x + 3) and write the result with the denominator in factored form.

Accepted Answer

(4x + 26)/((x + 3)(x + 6))

Answer

(4x + 24)/((x + 3)(x + 6))

Answer

6/((x + 3)(x + 6))

Answer

(4x + 26)/((x + 3)(x + 6)^2)

Question 26

Subtract 8/(x + 5) - 4/(x - 5) and write the result with the denominator in factored form.

Accepted Answer

(4x - 60)/((x + 5)(x - 5))

Answer

(4x - 20)/((x + 5)(x - 5))

Answer

(12x - 20)/((x + 5)(x - 5))

Answer

(12x - 60)/((x + 5)(x - 5))

Question 27

Add 5/(x + 1) + 6/(x + 5) and write the result with the denominator in factored form.

Accepted Answer

(11x + 31)/((x + 1)(x + 5))

Answer

(11x - 31)/((x + 1)(x + 5))

Answer

(11x - 19)/((x + 1)(x + 5))

Answer

11/((x + 1)(x + 5))

Question 28

Add 5/(x + 2) + 3/(x + 4) and write the result with the denominator in factored form.

Accepted Answer

(8x + 26)/((x + 2)(x + 4))

Answer

(8x - 26)/((x + 2)(x + 4))

Answer

(8x - 14)/((x + 2)(x + 4))

Answer

8/((x + 2)(x + 4))

Question 29

Add 5/(x - 3) + 2/(x - 5) and write the result with the denominator in factored form.

Accepted Answer

(7x - 31)/((x - 3)(x - 5))

Answer

(7x + 31)/((x - 3)(x - 5))

Answer

(7x + 19)/((x - 3)(x - 5))

Answer

7/((x - 3)(x - 5))

Question 30

Add 4/(x^2 + 7x + 6) + 3/(x + 1) and write the result with the denominator in factored form.

Accepted Answer

(3x + 22)/((x + 1)(x + 6))

Answer

(3x + 18)/((x + 1)(x + 6))

Answer

7/((x + 1)(x + 6))

Answer

(3x + 22)/((x + 1)(x + 6)^2)

Question 31

What is the least common denominator of 2/(x^2 - 16) and 7/(x^2 - 8x + 16)?

Accepted Answer

(x + 4)(x - 4)^2

Answer

(x + 4)(x - 4)

Answer

(x - 4)^2

Answer

(x^2 - 16)(x^2 - 8x + 16)

Question 32

Add 6/(x - 4) + 2/(x - 2) and write the result with the denominator in factored form.

Accepted Answer

(8x - 20)/((x - 4)(x - 2))

Answer

(8x + 20)/((x - 4)(x - 2))

Answer

(8x + 4)/((x - 4)(x - 2))

Answer

8/((x - 4)(x - 2))

Question 33

Add 3/(x + 5) + 7/(x + 1) and write the result with the denominator in factored form.

Accepted Answer

(10x + 38)/((x + 5)(x + 1))

Answer

(10x - 38)/((x + 5)(x + 1))

Answer

(10x + 32)/((x + 5)(x + 1))

Answer

10/((x + 5)(x + 1))

Question 34

A student writes 5/(x + 3) + 3/(x - 4) = 8/(2x - 1). What did the student do wrong?

Accepted Answer

added the denominators instead of rewriting both terms over a common denominator

Answer

used a common denominator that was not the least one

Answer

forgot to distribute a negative sign

Answer

canceled a factor that was not common to both terms

Question 35

What is the least common denominator of 5/(x^2 - 25) and 2/(x^2 + 10x + 25)?

Accepted Answer

(x - 5)(x + 5)^2

Answer

(x - 5)(x + 5)

Answer

(x + 5)^2

Answer

(x^2 - 25)(x^2 + 10x + 25)

Question 36

Add 3/(x + 2) + 2/(x - 3) and write the result with the denominator in factored form.

Accepted Answer

(5x - 5)/((x + 2)(x - 3))

Answer

(5x + 5)/((x + 2)(x - 3))

Answer

(5x + 13)/((x + 2)(x - 3))

Answer

5/((x + 2)(x - 3))

Question 37

Add 5/(x + 1) + 6/(x + 2) and write the result with the denominator in factored form.

Accepted Answer

(11x + 16)/((x + 1)(x + 2))

Answer

(11x - 16)/((x + 1)(x + 2))

Answer

(11x - 4)/((x + 1)(x + 2))

Answer

11/((x + 1)(x + 2))

Question 38

What is the least common denominator of 2/(x^2 - 9) and 7/(x^2 - x - 6)?

Accepted Answer

(x - 3)(x + 3)(x + 2)

Answer

(x - 3)

Answer

(x + 3)(x + 2)

Answer

(x^2 - 9)(x^2 - x - 6)

Question 39

Subtract 7/(x + 5) - 3/(x - 5) and write the result with the denominator in factored form.

Accepted Answer

(4x - 50)/((x + 5)(x - 5))

Answer

(4x - 20)/((x + 5)(x - 5))

Answer

(10x - 20)/((x + 5)(x - 5))

Answer

(10x - 50)/((x + 5)(x - 5))

Question 40

Add 7/(x^2 - 8x + 12) + 3/(x - 2) and write the result with the denominator in factored form.

Accepted Answer

(3x - 11)/((x - 2)(x - 6))

Answer

(3x - 18)/((x - 2)(x - 6))

Answer

10/((x - 2)(x - 6))

Answer

(3x - 11)/((x - 2)(x - 6)^2)

BLASTROOM

BLASTROOM

BLASTROOM

Adding and Subtracting Rational Expressions

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Adding and Subtracting Rational Expressions

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner