Integrated Algebra Quiz - Dividing Rational Expressions

Find the fully factored simplified quotient when you divide: 

 $\frac{x^2-2x-8}{x^2-2x-15}\$     by      $\frac{2x^2-8x}{2x^2-10x}$  

•  $\frac{2\left(x-2\right)}{2\left(x+3\right)}\$  

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

•  $\frac{x-2}{x+3}\$  

•  $\frac{x+2}{x+3}\$  

•  $\frac{2x+4}{2x+6}$  

Find the fully factored simplified quotient when you divide: 

 $\frac{a^2-5a-14}{a-7}\$     by      $\frac{a^2-a-6}{5a^3+30a^2}$  

•  $\frac{a+9}{15a}\$  

•  $\frac{5a^2\left(a+6\right)}{a-3}\$  

•  $\frac{1}{a-1}\$  

•  $\frac{9a}{a-3}\$  

•  $\frac{5a^3+30a^2}{a-3}$  

Find the fully factored simplified quotient when you divide: 

 $\frac{g+8}{6g+60}\$  by   $\frac{g^2-64}{g^2+2g-80}$  

•  $\frac{1}{6}\$  

•  $\frac{g+8}{6g+60}\$  

•  $\frac{g+10}{6g+60}\$  

•  $6$  

•  $\frac{6}{6g+60}$  

Find the fully factored simplified quotient when you divide: 

 $\frac{2q^2-4q-6}{3q^3-9q^2}\$     by      $\frac{4q^2+2q-2}{2q+1}$  

•  $\frac{1}{3q^2}\$  

•  $\frac{2q-1}{3q^2\left(2q+1\right)}\$  

•  $3q^2\$  

•  $\frac{2q+1}{6q^3-3q^2}$  

•  $\frac{2q+1}{3q^2\left(2q-1\right)}$  

Find the fully factored simplified quotient when you divide: 

 $\frac{3q^3-9q^2+5q-15}{q^2-9}\$     by      $\frac{6q^3+10q}{q^2}$  

•  $\frac{q}{2\left(q+3\right)}\$  

•  $\frac{q}{2q+6}\$  

•  $\frac{2q+6}{2}\$  

•  $q$  

•  $\frac{1}{2q^2}$  

Find the fully factored simplified quotient when you divide: 

 $\frac{5n^2-33n-14}{8n^2+12n}\$     by      $\frac{2n^2-17n+21}{4n^2-9}$  

•  $\frac{5n+2}{4n}\$  

•  $\frac{5n+2}{8n^2+12n}\$  

•  $\frac{n-7}{n}\$  

•  $5n+2$  

•  $\frac{4n}{5n+2}$  

Find the fully factored simplified quotient when you divide: 

 $\frac{5n^2+10n}{6n^2-24}\$     by      $\frac{5n^2-22n-15}{n^2-7n+10}$  

•  $\frac{5n}{30n+18}\$  

•  $\frac{5n}{5n+3}\$  

•  $\frac{5n}{6\left(5n+3\right)}\$  

•  $\frac{5}{30n+18}$  

•  $\frac{5}{6\left(5n+3\right)}$  

Find the fully factored simplified quotient when you divide: 

 $\frac{q^2+6q+9}{4q^2+13q+3}\$     by     $\left(7q^2+27q+18\right)$  

•  $\frac{1}{28q^2+31q+6}\$  

•  $\frac{1}{\left(4q+1\right)\left(7q+6\right)}\$  

•  $28q^2+31q+6$  

•  $\frac{q+3}{28q^2+31q+6}$  

•  $\frac{1}{7q+6^{ }}$  

Find the fully factored simplified quotient when you divide: 

 $\left(6a^2+5a-6\right)\$     by      $\frac{2a^2+13a+15}{a^2-25}$  

•  $\left(3a-2\right)\left(a-5\right)$  

•  $3a^2-17a+10$  

•  $\frac{3a+2}{a^2-25}\$  

•  $\left(2a+3\right)\left(a+5\right)$  

•  $2a^2+17a+15$  

Which of the following statements are true when dividing rational expressions. Select all that apply.

• Flip the first rational expression

• Change division to multiplication

• Factor all numerators and denominators

• Keep the second rational expression the same

• Flip the second rational expression