Multiply and Divide Rational Expressions (6-2)

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.D.6

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: 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.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

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.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

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.B.3