Rational Expressions and Equations

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.D.7

 $\frac{4x}{x-5}-\frac{3}{x-6}$  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.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.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.7

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

 $\frac{1}{5n^2}+\frac{2}{5n}=\frac{n+5}{n^2}$  Solve. Check for extraneous solutions.

•  $n\ =\ 4$  

•  $n\ =\ 8$  

•  $n\ =\ 2$  

•  $n=-8$  

Tags

CCSS.HSA.REI.A.2

Solve:  $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$  

•  $x=-5$  

•  $x=5$  

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

• No Solution

Tags

CCSS.HSA.REI.A.2