Integrated Algebra Quiz Multiplying Rational Expressions

What is the product of  $\frac{10q}{q-8}$  and  $\frac{6q^2-47q-8}{5q}$  in simplest fully factored form?  

•  $\frac{2}{6q+1}$  

•  $\frac{2q}{6q+1}$  

•  $2\left(6q+1\right)$  

•  $12q+2$  

•  $2\left(6q-1\right)$  

What is the product of  $\frac{x+8}{6x+60}$ and  $\frac{x^2+2x-80}{x^2-64}$ 
in simplest fully factored form? 

•  $\frac{1}{6}$  

•  $\frac{x+10}{6x+60}$  

•  $\frac{x+8}{6x+60}$  

•  $\frac{x+8}{6\left(x+10\right)}$  

•  $6$  

What is the product of  $\left(5g^2+13g-6\right)$  and  $\frac{g^2-4}{5g^2+8g-4}$  in simplest fully factored form?  

•  $g^2+g-6$  

•  $\frac{1}{g^2+3g-6}$  

•  $\left(g+3\right)\left(g-2\right)$  

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

•  $\frac{1}{g^2+g-6}$  

What is the product of  $\frac{3a^3+18a^2-4a-24}{4a-4}$  and  $\frac{4}{a^2+8a+12}$  in simplest fully factored form?  

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

•  $\frac{3a^2-4}{a^2+a-2}$  

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

•  $\frac{3a^2}{4a-4}$  

What is the product of  $\frac{a^2+7a+10}{a^2-5a-14}$  and  $\frac{a^2-6a-7}{a^2+6a+5}$  in simplest fully factored form?  

•  $\frac{\left(a+5\right)\left(a+1\right)}{\left(a-7\right)\left(a+2\right)}$  

•  $\frac{a-7}{a+5}$  

•  $\frac{a^2+6a+5}{a^2-5a-14}$  

•  $1$  

•  $\frac{1}{a-7}$  

What is the product of  $\frac{8g^2-6g}{g-4}$  and  $\frac{g^2-4g-5}{4g^2+g-3}$  in simplest fully factored form?  

•  $\frac{2g^2-10g}{g-4}$  

•  $\frac{2g^2-5}{g-4}$  

•  $2g^2+2g$  

•  $\frac{2g\left(g-5\right)}{g-4}$  

•  $\frac{2\left(g-5\right)}{g-4}$  

What are the steps for Multiplying Rational Expressions?

• Factor All Numerators

  Factor All Denominators

  Cancel/Reduce Common Factors

• Factor All Denominators

  Cancel/Reduce Common Factors

  Factor All Numerators

• Factor All Numerators

  Cancel/Reduce Common Factors

  Denominators are Already Factored

• Factor All Numerators

  Cancel/Reduce Common Factors

  Factor All Denominators

What is the product of  $\frac{a^2+10a+21}{a^2-4a+4}$  and  $\frac{a^2-4}{a^2+a-6}$  in simplest fully factored form?  

•  $\frac{a^2+10a+21}{a^2-4a+4}$  

•  $\frac{\left(a+2\right)\left(a+7\right)}{\left(a-2\right)\left(a-2\right)}$  

•  $\frac{\left(a+2\right)\left(a+7\right)}{a-2}$  

•  $\left(a+7\right)\left(a+2\right)$  

•  $a+3$  

What is the product of  $\frac{2q+1}{q^2-1}$  and  $\frac{q+1}{2q^2+q}$  in simplest fully factored form?  

•  $\frac{1}{q^2-q}$  

•  $\frac{1}{q}$  

•  $\frac{q-1}{q+1}$  

•  $\frac{1}{q\left(q-1\right)}$  

•  $q\left(q-1\right)$  

What is the product of  $\frac{a^2+6a}{6a^2+15a}$  and  $\frac{2a^2+7a+5}{a^2-36}$  in simplest fully factored form?  

•  $\frac{a+1}{3\left(a-6\right)}$  

•  $\frac{1}{2a-9}$  

•  $\frac{a+1}{3a-18}$  

•  $\frac{2a+5}{3a-18}$  

•  $\frac{a+1}{a-6}$