Rational Expressions

Simplify  $\frac{7n}{3n-18}+\frac{n+3}{3}$  

•  $\frac{8n+3}{3n-15}$  

•  $\frac{n^2+4n-18}{3\left(n-6\right)}$  

•  $\frac{7\left(n+3\right)}{3\left(3n-18\right)}$  

•  $\frac{7n+n+3}{3n-18+3}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

Simplify $\frac{8n}{n-3}+\frac{3n}{5n-6}$  

•  $\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}$  

•  $\frac{11n}{6n-9}$  

•  $\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}$  

•  $\frac{8n+3n}{n-3+5n-6}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $\frac{4x}{x-5}-\frac{3}{x-6}$  Simplify

•  $\frac{4x^2-27x+15}{\left(x-6\right)\left(x-5\right)}$  

•  $\frac{4x-3}{2x+1}$  

•  $\frac{4x^2-27x+21}{\left(x-6\right)\left(x-5\right)}$  

•  $\frac{4x^2+21x+15}{\left(x-5\right)\left(x+6\right)}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.B.3

 $2-\frac{7}{x^2+x-30}$  Simplify

•  $\frac{2x^2-2x-67}{\left(x-6\right)\left(x+5\right)}$  

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

•  $\frac{-5}{x^2+x-30}$  

•  $\frac{2x^2+2x-67}{\left(x+6\right)\left(x-5\right)}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Simplify  $\frac{1}{n+5}\times\frac{n^2+2n-15}{n-8}$  

•  $\frac{n-3}{n-8}$  

•  $\frac{n-3}{\left(n+5\right)\left(n-8\right)}$  

•  $\frac{n^2+2n-15}{\left(n+5\right)\left(n-8\right)}$  

•  $\frac{n^2+2n-14}{2n-3}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

 $\frac{2a-20}{6a}\times\frac{a-9}{a-10}$  Simplify

•  $\frac{2a^2-180}{6a^2-60a}$  

•  $\frac{2\left(a-9\right)}{6a}$  

•  $\frac{a-9}{3a}$  

•  $\frac{3a-29}{7a-10}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{m^2+m-30}{m^2+13m\ +42}\div\frac{m-2}{m+7}$  Simplify

•  $\frac{m-5}{m-2}$  

•  $\frac{\left(m-5\right)\left(m-2\right)}{\left(m+7\right)^2}$  

•  $\frac{m^2+2m-32}{m^2+14m+49}$  

•  $\frac{-5}{2m^2}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

 $\frac{2}{8m^3-64m^2}\div\frac{1}{8m^2}$  

•  $\frac{2}{m-64m^2}$  

•  $\frac{16m^2}{8m^2\left(m-8\right)}$  

•  $\frac{2}{64m^4\left(m-8\right)}$  

•  $\frac{2}{m-8}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

 $\frac{\frac{x+1}{x^2}}{\frac{1}{x}+\frac{x+1}{x}}$  Simplify

•  $\frac{\frac{x+1}{x^2}}{\frac{x+2}{x}}$  

•  $\frac{x+1}{x\left(x+2\right)}$  

•  $\frac{2x+2}{x\left(x+2\right)}$  

•  $\frac{1}{x}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

 $\frac{m}{\frac{1}{3}+\frac{18}{m}}$  Simplify

•  $\frac{3m^2}{m+54}$  

•  $\frac{m}{\frac{m+54}{3m}}$  

•  $\frac{3}{m+54}$  

•  $\frac{3m^2}{19}$  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3