91Ó°ÊÓ

In the following exercises, find the domain of each function.

$R\left(x\right)=\frac{x^3+3x^2-4x-12}{x^2-4}$

In the following exercises, find the domain of each function.

$R\left(x\right)=\frac{3x^2+15x}{6x^2+6x-36}$

In the following exercises, find the domain of each function.

$R\left(x\right)=\frac{8x^2-32x}{2x^2-6x-80}$

For the following exercises, find $R\left(x\right)=f\left(x\right).g\left(x\right)$where $f\left(x\right)andg\left(x\right)$are given.

localid="1644679377284" $f\left(x\right)=\frac{6x^2-12x}{x^2+7x-18}andg\left(x\right)=\frac{x^2-81}{3x^2-27x}$

For the following exercises, find $R\left(x\right)=f\left(x\right)g\left(x\right)$where $f\left(x\right)andg\left(x\right)$are given.

$f\left(x\right)=\frac{x^2-2x}{x^2+6x-16}andg\left(x\right)=\frac{x^2-64}{x^2-8x}$

For the following exercises, find$R\left(x\right)=f\left(x\right).g\left(x\right)$where$f\left(x\right)andg\left(x\right)$are given.

$f\left(x\right)=\frac{4x}{x^2-3x-10}andg\left(x\right)=\frac{x^2-25}{8x^2}$

For the following exercises, find $R\left(x\right)=f\left(x\right)g\left(x\right)$where $f\left(x\right)andg\left(x\right)$are given.

$f\left(x\right)=\frac{2x^2+8x}{x^2-9x+20}andg\left(x\right)=\frac{x-5}{x^2}$

For the following exercises, find $R\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$where $f\left(x\right)$and $g\left(x\right)$are given.

localid="1644858875634" $$\begin{gathered} f\left(x\right)=\frac{27x^2}{3x-21} \\ g\left(x\right)=\frac{3x^2+18x}{x^2+13x+42} \end{gathered}$$

For the following exercises, find $R\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$where $f\left(x\right)$and $g\left(x\right)$are given.

role="math" localid="1646212760399" $$\begin{gathered} f\left(x\right)=\frac{24x^2}{2x+8} \\ g\left(x\right)=\frac{4x^3+28x^2}{x^2+11x+28} \end{gathered}$$

In the following exercises, find $R\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$where $f\left(x\right)$and $g\left(x\right)$are known.

$$\begin{gathered} f\left(x\right)=\frac{16x^2}{4x+36} \\ g\left(x\right)=\frac{4x^2-24x}{x^2+4x-45} \end{gathered}$$