Operations with Rational Expressions

Find the difference of $\frac{6}{y-5}$  and $\frac{y+5}{y^2-25}$  

•  $\frac{5}{y-5}$  

•  $\frac{5}{y+5}$  

•  $\frac{5y}{y-5}$  

•  $\frac{5y}{y+5}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

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

Find the quotient of $\frac{n-4}{7n^2-28n}$  and  $\frac{3n}{n-2}$  

•  $\frac{5n^2}{8}$  

•  $\frac{n-2}{21n^2}$  

•  $5n$  

•  $\frac{5n}{n+1}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

• n = 0

• n = -7

• n = 2

• n = 4

Find the simplified product of $\frac{x^2+4x-5}{x-3}$  and  $\frac{x-3}{10x+50}$  

•  $\frac{x+1}{10}$  

•  $\frac{x^2+4x-5}{10x+50}$  

•  $\frac{x^2+5x-8}{9x+47}$  

•  $\frac{x-1}{10}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Simplify $\frac{x^2+2x-15}{x+5}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find the product of $\frac{k^2+12k+32}{k^2+13k+40}$  and  $\frac{k^2+5k}{k^2+6k+8}$  

•  $\frac{k^2+5k}{k+2}$  

•  $\frac{k}{k^2+13k+40}$  

•  $\frac{1}{k+2}$  

•  $\frac{k}{k+2}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Find the quotient of  $\frac{s^2-2s}{s^2+3s-10}$ and $\frac{s-5}{s+5}$   

•  $\frac{s-2}{s-5}$  

•  $\frac{s-5}{s}$  

•  $\frac{s}{s-5}$  

•  $\frac{s-2}{s^2-5s}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Find the difference of $\frac{3}{x}$  and  $\frac{9}{x-6}$  

•  $\frac{12x-18}{x\left(x-6\right)}$  

•  $\frac{-6x-18}{x\left(x-6\right)}$  

•  $-x$  

•  $\frac{27x-6}{x\left(x-6\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Find the sum of  $\frac{6}{k-4}$  and  $\frac{k+8}{k^2+2k-24}$  

•  $\frac{7k}{k-4}$  

•  $\frac{k+14}{k^2+3k-28}$  

•  $\frac{7k+44}{\left(k-4\right)\left(k+6\right)}$  

•  $\frac{7k+20}{\left(k-4\right)\left(k+6\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7