Chapter 7

Find each product and simplify if possible. $$ \frac{3 x}{y^{2}} \cdot \frac{7 y}{4 x} $$

Simplify each complex fraction. See Examples 1 and 2. $$ \frac{\frac{10}{3 x}}{\frac{5}{6 x}} $$

Find the domain of each rational expression. See Example 1. $$ f(x)=\frac{5 x-7}{4} $$

Solve each proportion. See Examples 1 and \(2 .\) $$ \frac{2}{3}=\frac{x}{6} $$

Solve each equation and check each solution. See Examples 1 through 3. \(\frac{x}{5}+3=9\)

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{a+1}{13}+\frac{8}{13} $$

Find each product and simplify if possible. $$ \frac{9 x^{2}}{y} \cdot \frac{4 y}{3 x^{3}} $$

Find the domain of each rational expression. See Example 1. $$ g(x)=\frac{4-3 x}{2} $$

Solve each proportion. See Examples 1 and \(2 .\) $$ \frac{x}{2}=\frac{16}{6} $$

Solve each equation and check each solution. See Examples 1 through 3. \(\frac{x}{5}-2=9\)

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3$$ \frac{x+1}{7}+\frac{6}{7} $$

Find the domain of each rational expression. See Example 1. $$ s(t)=\frac{t^{2}+1}{2 t} $$

Solve each proportion. See Examples 1 and \(2 .\) $$ \frac{x}{10}=\frac{5}{9} $$

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{4 m}{3 n}+\frac{5 m}{3 n} $$

Find each product and simplify if possible. $$ \frac{8 x}{2} \cdot \frac{x^{5}}{4 x^{2}} $$

Find the domain of each rational expression. See Example 1. $$ v(t)=-\frac{5 t+t^{2}}{3 t} $$

Solve each proportion. See Examples 1 and \(2 .\) $$ \frac{9}{4 x}=\frac{6}{2} $$

Solve each equation and check each solution. See Examples 1 through 3. \(\frac{x}{6}+\frac{4 x}{3}=\frac{x}{18}\)

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{3 p}{2 q}+\frac{11 p}{2 q} $$

Find each product and simplify if possible. $$ \frac{6 x^{2}}{10 x^{3}} \cdot \frac{5 x}{12} $$

Solve each proportion. See Examples 1 and \(2 .\) $$ \frac{x+1}{2 x+3}=\frac{2}{3} $$

Solve each equation and check each solution. See Examples 1 through 3. \(2-\frac{8}{x}=6\)

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{4 m}{m-6}-\frac{24}{m-6} $$

Find each product and simplify if possible. $$ -\frac{5 a^{2} b}{30 a^{2} b^{2}} \cdot b^{3} $$

Find the domain of each rational expression. See Example 1. $$ f(x)=\frac{-4 x}{-2+x} $$

Solve each proportion. See Examples 1 and \(2 .\) $$ \frac{x+1}{x+2}=\frac{5}{3} $$

Solve each equation and check each solution. See Examples 1 through 3. \(5+\frac{4}{x}=1\)

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{8 y}{y-2}-\frac{16}{y-2} $$

Find each product and simplify if possible. $$ -\frac{9 x^{3} y^{2}}{18 x y^{5}} \cdot y^{3} $$

Find the domain of each rational expression. See Example 1. $$ f(x)=\frac{x}{3 x-1} $$

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{9}{3+y}+\frac{y+1}{3+y} $$

Find each product and simplify if possible. $$ \frac{x}{2 x-14} \cdot \frac{x^{2}-7 x}{5} $$

Find the domain of each rational expression. See Example 1. $$ g(x)=\frac{-2}{2 x+5} $$

Perform each indicated operation. Simplify if possible. See Examples I through 7. $$ \frac{8}{x+4}-\frac{3}{3 x+12} $$

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{9}{y+9}+\frac{y-5}{y+9} $$

Find each product and simplify if possible. $$ \frac{4 x-24}{20 x} \cdot \frac{5}{x-6} $$

Simplify each complex fraction. See Examples 1 and 2. $$ \frac{\frac{4 x^{2}-y^{2}}{x y}}{\frac{2}{y}-\frac{1}{x}} $$

Solve. See Example 3 The ratio of the weight of an object on Earth to the weight of the same object on Pluto is 100 to \(3 .\) If an elephant weighs 4100 pounds on Earth, find the elephant's weight on Pluto.

Find each product and simplify if possible. $$ \frac{6 x+6}{5} \cdot \frac{10}{36 x+36} $$

Perform each indicated operation. Simplify if possible. See Examples I through 7. $$ \frac{3}{x-4}+\frac{4 x}{x^{2}-16} $$

Solve. See Example 3 If a 170 -pound person weighs approximately 65 pounds on Mars, about how much does a 9000 -pound satellite weigh? Round your answer to the nearest pound.

Solve each equation and check each solution. See Examples 1 through 3. \(\frac{b}{5}=\frac{b+2}{6}\)

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{x^{2}+9 x}{x+7}-\frac{4 x+14}{x+7} $$

Find each product and simplify if possible. $$ \frac{x^{2}+x}{8} \cdot \frac{16}{x+1} $$

Solve each equation and check each solution. See Examples 1 through 3. \(\frac{x-3}{5}+\frac{x-2}{2}=\frac{1}{2}\)

Add or subtract as indicated. Simplify the result if possible. See Examples 1 through 3. $$ \frac{4 a}{a^{2}+2 a-15}-\frac{12}{a^{2}+2 a-15} $$

Find each product and simplify if possible. $$ \frac{(m+n)^{2}}{m-n} \cdot \frac{m}{m^{2}+m n} $$

Simplify each complex fraction. See Examples 1 and 2. $$ \frac{\frac{x+3}{12}}{\frac{4 x-5}{15}} $$

Solve. See Example 3 On an architect's blueprint, 1 inch corresponds to 4 feet. Find the length of a wall represented by a line that is \(3 \frac{7}{8}\) inches long on the blueprint.

Solve each equation and check each solution. See Examples 1 through 3. \(\frac{a+5}{4}+\frac{a+5}{2}=\frac{a}{8}\)