Chapter 7

$$ \frac{a}{13}+\frac{9}{13} $$

Find the value of the following expressions when \(x=2, y=-2,\) and \(z=-5\). $$ \frac{x+5}{x+2} $$

Simplify each complex fraction. $$ \frac{\frac{1}{2}}{\frac{3}{4}} $$

Find each product and simplify if possible. See Examples 1 through 3. $$ \frac{3 x}{y^{2}} \cdot \frac{7 y}{4 x} $$

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

Solve each proportion. $$ \frac{2}{3}=\frac{x}{6} $$

Perform each indicated operation. Simplify if possible. \(\frac{4}{2 x}+\frac{9}{3 x}\)

$$ \frac{x+1}{7}+\frac{6}{7} $$

Find the value of the following expressions when \(x=2, y=-2,\) and \(z=-5\). $$ \frac{x+8}{x+1} $$

Simplify each complex fraction. $$ \frac{\frac{1}{8}}{-\frac{5}{12}} $$

Find each product and simplify if possible. See Examples 1 through 3. $$ \frac{9 x^{2}}{y} \cdot \frac{4 y}{3 x^{3}} $$

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

Solve each proportion. $$ \frac{x}{2}=\frac{16}{6} $$

Perform each indicated operation. Simplify if possible. \(\frac{15}{7 a}+\frac{8}{6 a}\)

$$ \frac{4 m}{3 n}+\frac{5 m}{3 n} $$

Find the value of the following expressions when \(x=2, y=-2,\) and \(z=-5\). $$ \frac{y^{3}}{y^{2}-1} $$

Simplify each complex fraction. $$ \frac{-\frac{4 x}{9}}{-\frac{2 x}{3}} $$

Find each product and simplify if possible. See Examples 1 through 3. $$ \frac{8 x}{2} \cdot \frac{x^{5}}{4 x^{2}} $$

Solve each equation and check each solution. See Examples 1 through 3. $$ \frac{x}{2}+\frac{5 x}{4}=\frac{x}{12} $$

Solve each proportion. $$ \frac{x}{10}=\frac{5}{9} $$

Perform each indicated operation. Simplify if possible. \(\frac{15 a}{b}+\frac{6 b}{5}\)

$$ \frac{3 p}{2 q}+\frac{11 p}{2 q} $$

Find the value of the following expressions when \(x=2, y=-2,\) and \(z=-5\). $$ \frac{z}{z^{2}-5} $$

Simplify each complex fraction. $$ \frac{-\frac{6 y}{11}}{\frac{4 y}{9}} $$

Find each product and simplify if possible. See Examples 1 through 3. $$ \frac{6 x^{2}}{10 x^{3}} \cdot \frac{5 x}{12} $$

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

Solve each proportion. $$ \frac{9}{4 x}=\frac{6}{2} $$

Perform each indicated operation. Simplify if possible. \(\frac{4 c}{d}-\frac{8 d}{5}\)

$$ \frac{4 m}{m-6}-\frac{24}{m-6} $$

Find the value of the following expressions when \(x=2, y=-2,\) and \(z=-5\). $$ \frac{x^{2}+8 x+2}{x^{2}-x-6} $$

Simplify each complex fraction. $$ \frac{\frac{1+x}{6}}{\frac{1+x}{3}} $$

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

Solve each proportion. $$ \frac{x+1}{2 x+3}=\frac{2}{3} $$

Perform each indicated operation. Simplify if possible. \(\frac{3}{x}+\frac{5}{2 x^{2}}\)

$$ \frac{8 y}{y-2}-\frac{16}{y-2} $$

Find the value of the following expressions when \(x=2, y=-2,\) and \(z=-5\). $$ \frac{x+5}{x^{2}+4 x-8} $$

Simplify each complex fraction. $$ \frac{\frac{6 x-3}{5 x^{2}}}{\frac{2 x-1}{10 x}} $$

Find each product and simplify if possible. See Examples 1 through 3. $$ -\frac{9 x^{3} y^{2}}{18 x y^{5}} \cdot y^{3} $$

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

Solve each proportion. $$ \frac{x+1}{x+2}=\frac{5}{3} $$

Perform each indicated operation. Simplify if possible. \(\frac{14}{3 x^{2}}+\frac{6}{x}\)

$$ \frac{9}{3+y}+\frac{y+1}{3+y} $$

The average cost per DVD, in dollars, for a company to produce \(x\) DVDs on exercising is given by the formula \(A=\frac{3 x+400}{x},\) where \(A\) is the average cost per DVD and \(x\) is the number of DVDs produced. a. Find the cost for producing \(1 \mathrm{DVD}\). b. Find the average cost for producing 100 DVDs. c. Does the cost per DVD decrease or increase when more DVDs are produced? Explain your answer.

Simplify each complex fraction. $$ \frac{\frac{1}{2}+\frac{2}{3}}{\frac{5}{9}-\frac{5}{6}} $$

Find each product and simplify if possible. See Examples 1 through 3. $$ \frac{x}{2 x-14} \cdot \frac{x^{2}-7 x}{5} $$

Solve each proportion. $$ \frac{9}{5}=\frac{12}{3 x+2} $$

Perform each indicated operation. Simplify if possible. \(\frac{6}{x+1}+\frac{10}{2 x+2}\)

$$ \frac{9}{y+9}+\frac{y-5}{y+9} $$

For a certain model of fax machine, the manufacturing cost \(C\) per machine is given by the equation $$ C=\frac{250 x+10,000}{x} $$ where \(x\) is the number of fax machines manufactured and \(\operatorname{cost} C\) is in dollars per machine. a. Find the cost per fax machine when manufacturing 100 fax machines. b. Find the cost per fax machine when manufacturing 1000 fax machines. c. Does the cost per machine decrease or increase when more machines are manufactured? Explain why this is so.

Simplify each complex fraction. $$ \frac{\frac{3}{4}-\frac{1}{2}}{\frac{3}{8}+\frac{1}{6}} $$