Operations on Rational Expressions

Simplify:  $\frac{36y}{72z}$  

•  $\frac{4y}{9z}$  

•  $\frac{y}{2z}$  

•  $\frac{2y}{3z}$  

•  $\frac{18y}{38z}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify: $\frac{x-y}{y-x}$  

•  $\frac{x-y}{y-x}$  

•  $\frac{1}{-x}$  

•  $-1$  

•  $\frac{-1}{y}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify: $\frac{b^2-b-6}{b^2+4b+4}$  

•  $\frac{b-6}{b+4}$  

•  $\frac{b+3}{b+2}$  

•  $\frac{b+3}{b+4}$  

•  $\frac{b-3}{b+2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

Simplify: $\frac{r^3+j^3}{r^2-ry+j^2}$  

•  $\frac{r+j}{r-j}$  

•  $\frac{\left(r^2+rj+j^2\right)}{\left(r-2j\right)}$  

•  $r+j$  

•  $\frac{\left(r+j\right)\left(r^2+rj+j^2\right)}{\left(r-2j\right)\left(r+j\right)}$  

Find the product: $\frac{x-4}{x+7}\times\frac{x-3}{x-8}$  

•  $\frac{x^2-7x+12}{x^2-x-56}$  

•  $\frac{x^2-12x+32}{x^2+4x-21}$  

•  $\frac{x^2+7x+12}{x^2-56}$  

•  $\frac{x^2-12x+32}{x^2-21}$  

Tags

CCSS.HSA.APR.D.7

Find the product: $\frac{a+b}{a^3+b^3}\times\frac{a^2-ab+b^2}{a-b}$  

•  $\frac{a+b}{a^2-b^2}$  

•  $\frac{1}{a-b}$  

•  $a+b$  

• 1

Find the quotient: $\frac{a^2-4}{3a}\div\frac{5a^2}{a-2}$  

•  $\frac{5a\left(a+4\right)}{3}$  

•  $\frac{a^3-2a^2-4a+8}{15a^3}$  

•  $\frac{5a^2+20a}{3}$  

•  $\frac{a^3-6a+8}{15a}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Simplify: $\frac{\frac{m^2-4n^2}{m+2n}}{\frac{1}{m+2n}}$  

•  $\frac{m^2-4n^2}{m^2+4mn+n^2}$  

•  $\frac{m-2n}{m+2n}$  

•  $\frac{m+2n}{m-2n}$  

•  $m^2-4n^2$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

Subtract: $\frac{9x+1}{x-2}-\frac{3x-4}{x-2}$  

•  $\frac{6x-3}{x-2}$  

•  $\frac{12x+5}{x-2}$  

•  $\frac{6x+5}{x-2}$  

•  $\frac{12x-3}{x-2}$  

Tags

CCSS.HSA.APR.D.7

Find the sum: $\frac{x}{x+1}+\frac{2x}{x+2}$  

•  $\frac{3x}{2x+3}$  

•  $\frac{3x^2+4x}{\left(x+1\right)\left(x+23\right)}$  

•  $\frac{3x}{\left(x+1\right)\left(x+23\right)}$  

•  $\frac{3x^2+4x}{\left(x+1\right)\left(x+2\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7