Chapter 9

Simplify each sum. \(\frac{5 x}{x^{2}-x-6}+\frac{4}{x^{2}+4 x+4}\)

Sketch the asymptotes and the graph of each equation. \(y=\frac{-2}{x}-3\)

Suppose that \(x\) and \(y\) vary inversely. Write a function that models each inverse variation and find \(y\) when \(x=10 .\) $$ x=5 \text { when } y=-\frac{1}{3} $$

\(\boldsymbol{S}\) and \(\boldsymbol{T}\) are mutually exclusive events. Find \(\boldsymbol{P}(\boldsymbol{S} \text { or } \boldsymbol{T})\) $$ P(S)=12 \%, P(T)=27 \% $$

Solve each equation. Check each solution. $$ \frac{3}{2 x}-\frac{5}{3 x}=2 $$

Divide. State any restrictions on the variables. $$ \frac{3 y-12}{2 y+4} \div \frac{6 y-24}{4 y+8} $$

Describe the vertical asymptotes and holes for the graph of each rational function. $$ y=\frac{9-x^{2}}{x^{2}-9} $$

Simplify each difference. \(\frac{-2}{x}-\frac{1}{x}\)

Sketch the asymptotes and the graph of each equation. \(y=\frac{1}{x-2}+5\)

Describe the combined variation that is modeled by each formula. $$ A=\pi r^{2} $$

\(\boldsymbol{S}\) and \(\boldsymbol{T}\) are mutually exclusive events. Find \(\boldsymbol{P}(\boldsymbol{S} \text { or } \boldsymbol{T})\) $$ P(S)=\frac{1}{7}, P(T)=60 \% $$

Solve each equation. Check each solution. $$ \frac{5 x}{4}-\frac{3}{x}=\frac{1}{4} $$

Divide. State any restrictions on the variables. $$ \frac{x^{2}}{x^{2}+2 x+1} \div \frac{3 x}{x^{2}-1} $$

Describe the vertical asymptotes and holes for the graph of each rational function. $$ y=\frac{2 x^{2}}{2 x^{2}+2} $$

Simplify each difference. \(\frac{-5 y}{2 y-1}-\frac{y+3}{2 y-1}\)

Sketch the asymptotes and the graph of each equation. \(y=\frac{1}{x-3}+4\)

A standard number cube is tossed. Find each probability. \(P(3 \text { or odd })\)

Solve each equation. Check each solution. $$ \frac{2}{y}+\frac{1}{2}=\frac{5}{2 y} $$

Divide. State any restrictions on the variables. $$ \frac{y^{2}-5 y+6}{y^{3}} \div \frac{y^{2}+3 y-10}{4 y^{2}} $$

Describe the vertical asymptotes and holes for the graph of each rational function. $$ y=\frac{6 x^{2}+x-2}{3 x^{2}+17 x+10} $$

Simplify each difference. \(\frac{y}{2 y+4}-\frac{3}{y+2}\)

Describe the combined variation that is modeled by each formula. $$ h=\frac{2 A}{b} $$

Sketch the asymptotes and the graph of each equation. \(y=\frac{2}{x+6}-1\)

Solve each equation. Check each solution. $$ \frac{2}{y}+\frac{1}{2}=\frac{5}{2 y} $$

Simplify each rational expression. State any restrictions on the variables. $$ \frac{x^{2}-5 x-24}{x^{2}-7 x-30} $$

Find the horizontal asymptote of the graph of each rational function. $$ y=\frac{5}{x+6} $$

Simplify each difference. \(\frac{x}{3 x+9}-\frac{8}{x^{2}+3 x}\)

Describe the combined variation that is modeled by each formula. $$ V=\frac{B h}{3} $$

Sketch the asymptotes and the graph of each equation. \(y=\frac{-10}{x+1}-8\)

A standard number cube is tossed. Find each probability. \(P(4 \text { or even })\)

A standard number cube is tossed. Find each probability. \(P(\text { even or less than } 4)\)

Simplify each rational expression. State any restrictions on the variables. $$ \frac{2 y^{2}+8 y-24}{2 y^{2}-8 y+8} $$

Solve each equation. Check each solution. $$ \frac{1}{4 x}-\frac{3}{4}=\frac{7}{x} $$

Find the horizontal asymptote of the graph of each rational function. $$ y=\frac{x+2}{2 x^{2}-4} $$

Simplify each difference. \(\frac{3 y}{y^{2}-25}-\frac{8}{y-5}\)

Describe the combined variation that is modeled by each formula. $$ V=\pi r^{2} h $$

Sketch the asymptotes and the graph of each equation. \(y=\frac{1}{x}+2\)

A standard number cube is tossed. Find each probability. \(P(\text { odd or greater than } 2)\)

Simplify each rational expression. State any restrictions on the variables. $$ \frac{x y^{3}-9 x y}{12 x y^{2}+12 x y-144 x} $$

Solve each equation. Check each solution. $$ \frac{1}{4 x}-\frac{3}{4}=\frac{7}{x} $$

Simplify each difference. \(\frac{2 x}{x^{2}-x-2}-\frac{4 x}{x^{2}-3 x+2}\)

$$ y=\frac{x+1}{x+5} $$

Describe the combined variation that is modeled by each formula. $$ h=\frac{V}{\pi r^{2}} $$

Sketch the asymptotes and the graph of each equation. \(y=\frac{-8}{x+5}-6\)

A standard number cube is tossed. Find each probability. \(P(\text { odd or prime })\)

Carlos can travel 40 \(\mathrm{mi}\) on his motorbike in the same time it takes Paul to travel 15 \(\mathrm{mi}\) on his bicycle. If Paul rides his bike 20 \(\mathrm{mi} / \mathrm{h}\) slower than Carlos rides his motorbike, find the speed for each bike.

Simplify each complex fraction. \(\frac{\frac{1}{x}}{\frac{2}{y}}\)

Find the horizontal asymptote of the graph of each rational function. $$ y=\frac{x^{2}+2}{2 x^{2}-1} $$

Describe the combined variation that is modeled by each formula. $$ V=\ell w h $$

Write an equation for the translation of \(y=\frac{2}{x}\) that has the given asymptotes. \(x=0\) and \(y=4\)