Multiply and Divide Rational Expressions

 $\frac{x^2+10x+24}{x^2-x-20}$  Simplify.

• $\frac{x+6}{x+4}$

• $\left(x+6\right)\left(x+4\right)$

• $x+6$

• $\frac{x+6}{x-5}$

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Simplify $\frac{x+9}{x^2-81}$  

• $\frac{x-9}{x+9}$

• $\frac{1}{x-9}$

• $x+9$

• $\frac{1}{x+9}$

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Complete Step 1:  FACTOR
 $\frac{x^2\ -5x\ +\ 6}{x^2-4}\cdot\frac{\left(x\ +6\right)\left(x\ +\ 5\right)}{x^2+2x\ -15}$  

•  $\frac{\left(x\ -\ 3\right)\left(x\ -\ 2\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ +\ 5\right)\left(x\ -\ 3\right)}$  

•  $\frac{\left(x\ +\ 6\right)\left(x\ -\ 1\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ -5\right)\left(x\ -3\right)}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

Complete Step 2: State the Restrictions
 $\frac{\left(x-3\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\cdot\frac{\left(x+6\right)\left(x+5\right)}{\left(x+5\right)\left(x-3\right)}$  

•  $x\ne-2,\ 2,\ -5,\ 3$  

•  $x\ne2,\ -2,\ 5,\ -3$  

•  $x\ne3,\ 2,\ -6,\ -5$  

•  $x\ne-3,\ 2,\ -6,\ -5$  

Tags

CCSS.HSA.APR.D.7

Complete Step 3:  CANCEL
 $\frac{\left(x-3\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\cdot\frac{\left(x+6\right)\left(x+5\right)}{\left(x+5\right)\left(x-3\right)}$  

•  $\frac{x+6}{x+2}$  

•  $\frac{x+2}{x+6}$  

•  $\frac{\left(x-3\right)}{\left(x+2\right)}\cdot\frac{\left(x+6\right)}{\left(x-3\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Complete Step 1: Multiply by the reciprocal or KFC (Keep, Flip, Change)
 $\frac{3\left(x-9\right)}{x^2-36}\div\frac{x-9}{x^2-x-30}$  

•  $\frac{x^2-36}{3\left(x-9\right)}\cdot\frac{x^2-x-30}{x-9}$  

•  $\frac{3\left(x-9\right)}{x^2-36}\cdot\frac{x^2-x-30}{x-9}$  

Tags

CCSS.HSA.APR.D.7

Complete Step 2:  FACTOR
 $\frac{3\left(x-9\right)}{x^2-36}\cdot\frac{x^2-x-30}{x-9}$  

•  $\frac{3\left(x-9\right)}{\left(x+6\right)\left(x+6\right)}\cdot\frac{\left(x-5\right)\left(x-6\right)}{x-9}$  

•  $\frac{3\left(x-9\right)}{\left(x+6\right)\left(x-6\right)}\cdot\frac{\left(x-6\right)\left(x\ +5\right)}{x-9}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Complete Step 3:  State Restrictions
 $\frac{3\left(x-9\right)}{\left(x+6\right)\left(x-6\right)}\cdot\frac{\left(x-6\right)\left(x+5\right)}{x-9}$  

•  $x\ne-6,\ 6,\ 9$  

•  $x\ne6,\ -6,\ -9$  

•  $x\ne9,\ -6,\ -5$  

•  $x\ne-9,\ -6,\ 5$  

Tags

CCSS.HSA.APR.D.7

Complete Step 4:  CANCEL
 $\frac{3\left(x-9\right)}{\left(x+6\right)\left(x-6\right)}\cdot\frac{\left(x-6\right)\left(x+5\right)}{x-9}$  

•  $\frac{3\left(x+5\right)}{x+6}$  

•  $\frac{x+5}{x+6}$  

•  $\frac{3}{\left(x+6\right)\left(x+5\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{b-4}{b^2-14b+40}\div\frac{b^2+6b+8}{b^2-3b-70}$  

•  $\frac{b-3}{6}$  

•  $\frac{2b}{9}$  

•  $\frac{5b\left(b-6\right)}{7}$  

•  $\frac{b+7}{\left(b+4\right)\left(b+2\right)}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7