91Ó°ÊÓ

Simplify

In the following exercises, use either method.

$\frac{\frac{v}{w}+\frac{1}{v}}{\frac{1}{v}−\frac{v}{w}}$

Simplify

In the following exercises, use either method.

$\frac{\frac{2}{a+4}}{\frac{1}{a^2−16}}$

Simplify

In the following exercises, use either method.

$\frac{\frac{3}{b^2−3b−40}}{\frac{5}{b+5}−\frac{2}{b−8}}$

Simplify

In the following exercises, use either method.

$\frac{\frac{3}{m}+\frac{3}{n}}{\frac{1}{m^2}−\frac{1}{n^2}}$

Simplify

In the following exercises, use either method.

$\frac{{\displaystyle \frac{2}{r-9}}}{{\displaystyle \frac{1}{r+9}}+{\displaystyle \frac{3}{r^2-81}}}$.

Simplify

In the following exercises, use either method.

$\frac{x-{\displaystyle \frac{3x}{x+2}}}{{\displaystyle \frac{3}{x+2}}+{\displaystyle \frac{3}{x-2}}}$.

Simplify

In the following exercises, use either method.

$\frac{{\displaystyle \frac{y}{y+3}}}{2+{\displaystyle \frac{1}{y-3}}}$.

Electronics The resistance of a circuit formed by connecting two resistors in parallel is $\frac{1}{{\displaystyle \frac{1}{R_1}}+{\displaystyle \frac{1}{R_2}}}$.

1. Simplify the complex fraction role="math" localid="1647789125778" $\frac{1}{{\displaystyle \frac{1}{R_1}+\frac{1}{R_2}}}$.
2. Find the resistance of the circuit when $R_1=8$and $R_2=12$.

In the following exercises, determine the values for which the rational expression is undefined.

$$\begin{gathered} \left(a\right)\frac{4x^{2}y}{3y} \\ \left(b\right)\frac{3x-2}{2x+1} \\ \left(c\right)\frac{u-1}{u^2-3u-28} \end{gathered}$$

In the following exercises, simplify.

$\frac{8n-96}{3n-36}$