유리함수

Divide Rational Expressions

In the following exercises, divide the rational expressions.

$\frac{\frac{4{d}^{2}+7d-2}{35d+10}}{\frac{{d}^{2}-4}{7{d}^{2}-12d-4}}$

For the following exercises, perform the indicated operations.

$\frac{10{m}^{2}+80m}{3m-9}\cdot \frac{{m}^{2}+4m-21}{{m}^{2}-9m+20}\div \frac{5{m}^{2}+10m}{2m-10}$

For the following exercises, perform the indicated operations.

$\frac{4{n}^{2}+32n}{3n+2}\cdot \frac{3{n}^{2}-n-2}{{n}^{2}+n-30}\div \frac{108{n}^{2}-24n}{n+6}$

For the following exercises, perform the indicated operations.

$\frac{12{p}^{2}+3p}{p+3}\div \frac{{p}^{2}+2p-63}{{p}^{2}-p-12}\cdot \frac{p-7}{9{p}^{3}-9{p}^{2}}$

For the following exercises, perform the indicated operations.

$\frac{6q+3}{9{q}^{2}-9q}\div \frac{{q}^{2}+14q+33}{{q}^{2}+4q-5}\cdot \frac{4{q}^{2}+12q}{12q+6}$

Multiply and Divide Rational Functions

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

$R(x)=\frac{{x}^{3}-2{x}^{2}-25x+50}{{x}^{2}-25}$

Multiply and Divide Rational Functions

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

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

Multiply and Divide Rational Functions

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

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

Multiply and Divide Rational Functions

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

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

For the following exercises, find $R(x)=f(x)\cdot g(x)$ where $f(x)$ and $g(x)$ are given.

$f(x)=\frac{6{x}^{2}-12x}{{x}^{2}+7x-18}$ $\quad g(x)=\frac{{x}^{2}-81}{3{x}^{2}-27x}$

For the following exercises, find $R(x)=f(x)\cdot g(x)$ where $f(x)$ and $g(x)$ are given.

$f(x)=\frac{{x}^{2}-2x}{{x}^{2}+6x-16}$ $\quad g(x)=\frac{{x}^{2}-64}{{x}^{2}-8x}$

For the following exercises, find $R(x)=f(x)\cdot g(x)$ where $f(x)$ and $g(x)$ are given.

$f(x)=\frac{4x}{{x}^{2}-3x-10}$ $\quad g(x)=\frac{{x}^{2}-25}{8{x}^{2}}$

For the following exercises, find $R(x)=f(x)\cdot g(x)$ where $f(x)$ and $g(x)$ are given.

$f(x)=\frac{2{x}^{2}+8x}{{x}^{2}-9x+20}$ $\quad g(x)=\frac{x-5}{{x}^{2}}$

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

$f(x)=\frac{27{x}^{2}}{3x-21}$ $\quad g(x)=\frac{3{x}^{2}+18x}{{x}^{2}+13x+42}$

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

$f(x)=\frac{24{x}^{2}}{2x-8}$ $\quad g(x)=\frac{4{x}^{3}+28{x}^{2}}{{x}^{2}+11x+28}$

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

$f(x)=\frac{16{x}^{2}}{4x+36}$ $\quad g(x)=\frac{4{x}^{2}-24x}{{x}^{2}+4x-45}$

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

$f(x)=\frac{24{x}^{2}}{2x-4}$ $\quad g(x)=\frac{12{x}^{2}+36x}{{x}^{2}-11x+18}$

Explain how you find the values of x for which the rational expression $\frac{{x}^{2}-x-20}{{x}^{2}-4}$ is undefined.

Explain all the steps you take to simplify the rational expression $\frac{{p}^{2}+4p-21}{9-{p}^{2}}.$

ⓐ Multiply $\frac{7}{4}\cdot \frac{9}{10}$ and explain all your steps. ⓑ Multiply $\frac{n}{n-3}\cdot \frac{9}{n+3}$ and explain all your steps. ⓒ Evaluate your answer to part ⓑ when $n=7$. Did you get the same answer you got in part ⓐ ? Why or why not?