Chapter 6

Solve each equation for \(y\). $$\frac{y-5}{x+3}=-\frac{4}{3}$$

Solve each equation for \(y\). $$\frac{y+1}{x-9}=\frac{3}{4}$$

Reading and Writing After reading this section, write out the answers to these questions. Use complete sentences. How can an equation involving rational expressions have an extraneous root?

After reading this section, write out the answers to these questions. Use complete sentences. What is the domain of a rational expression?

Solve each equation for \(y\). $$M=\frac{1}{y}$$

Simplify each complex fraction. Use either method. $$\frac{\frac{1}{2}+\frac{1}{4}}{\frac{1}{2}+\frac{1}{8}}$$

Solve each equation for \(y\). $$L=\frac{a y}{w}$$

Simplify each complex fraction. Use either method. $$\frac{\frac{1}{3}+\frac{1}{4}}{\frac{1}{5}+\frac{1}{6}}$$

After reading this section, write out the answers to these questions. Use complete sentences. For which operations with rational expressions is it not necessary to have identical denominators?

Simplify each complex fraction. Use either method. $$\frac{\frac{1}{2}-\frac{1}{3}}{\frac{1}{4}-\frac{1}{5}}$$

Solve each equation for \(y\). $$\frac{1}{n}=\frac{a}{y}-\frac{w}{a}$$

Simplify each complex fraction. Use either method. $$\frac{\frac{1}{2}-\frac{1}{4}}{\frac{1}{6}-\frac{1}{8}}$$

Solve each equation for \(y\). $$h=\frac{b}{y}+3$$

Find the solution set to each equation. $$\frac{1}{x}+\frac{1}{6}=\frac{1}{8}$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{3 x}{2}+\frac{5 x}{2} $$

Simplify each complex fraction. Use either method. $$\frac{\frac{2}{3}+\frac{5}{6}-\frac{1}{2}}{\frac{1}{8}-\frac{1}{3}+\frac{1}{12}}$$

Find the domain of each rational expression. $$\frac{3 x}{x-1}$$

Find the solution set to each equation. $$\frac{3}{x}+\frac{1}{5}=\frac{1}{2}$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{5 x^{2}}{3}+\frac{4 x^{2}}{3} $$

Simplify each complex fraction. Use either method. $$\frac{\frac{2}{5}-\frac{x}{9}-\frac{1}{3}}{\frac{1}{3}+\frac{x}{5}+\frac{2}{15}}$$

Find the domain of each rational expression. $$\frac{x}{x+5}$$

$$\text { Solve each formula for the indicated variable.}$$ $$M=\frac{F}{f} \text { for } f$$

Find the solution set to each equation. $$\frac{2}{3 x}+\frac{1}{15 x}=\frac{1}{2}$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{7 x}{2}-\frac{9 x}{2} $$

Find the domain of each rational expression. $$\frac{2 z-5}{7 z}$$

$$\text { Solve each formula for the indicated variable.}$$ $$P=\frac{A}{1+r t} \text { for } A$$

Find the solution set to each equation. $$\frac{5}{6 x}-\frac{1}{8 x}=\frac{17}{24}$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{3 a}{4}-\frac{a}{4} $$

Find the domain of each rational expression. $$\frac{z-12}{4 z}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{1}{a}+\frac{1}{b}=\frac{1}{2} \text { for } a$$

Find the solution set to each equation. $$\frac{3}{x-2}+\frac{5}{x}=\frac{10}{x}$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{x-3}{2 x}-\frac{3 x-5}{2 x} $$

Find the domain of each rational expression. $$\frac{5 y-1}{y^{2}-4}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{2}{x}=\frac{3}{y}-w \text { for } y$$

Find the solution set to each equation. $$\frac{5}{x-1}+\frac{1}{2 x}=\frac{1}{x}$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{9-4 y}{3 y}-\frac{6-y}{3 y} $$

Find the domain of each rational expression. $$\frac{2 y-1}{y^{2}-9}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{1}{2 x}+\frac{1}{2}-\frac{2}{y}=0 \text { for } x$$

Find the solution set to each equation. $$\frac{x}{x-2}+\frac{3}{x}=2$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{3 x-4}{2 x-4}+\frac{2 x-6}{2 x-4} $$

Find the domain of each rational expression. $$\frac{x-1}{x^{2}+4}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{1}{x}-\frac{2}{3 y}+z=0 \text { for } y$$

Find the solution set to each equation. $$\frac{x}{x-5}+\frac{5}{x}=\frac{11}{6}$$

Find the domain of each rational expression. $$\frac{y+5}{y^{2}+9}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \text { for } R_{1}$$

Find the solution set to each equation. $$\frac{100}{x}=\frac{150}{x+5}-1$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{x^{2}+4 x-6}{x^{2}-9}-\frac{x^{2}+2 x-12}{x^{2}-9} $$

Which real numbers cannot be used in place of the variable in each rational expression? $$\frac{2 a-3}{a^{2}+5 a+6}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}} \text { for } R_{2}$$

Find the solution set to each equation. $$\frac{30}{x}=\frac{50}{x+10}+\frac{1}{2}$$