Chapter 11

Simplify the expression. $$\frac{2 x}{x-1}-\frac{7 x}{x+4}$$

Solve the equation by multiplying each side by the least common denominator. $$\frac{1}{x-4}+\frac{1}{x+4}=\frac{22}{x^{2}-16}$$

Solve the proportion. Check for extraneous solutions. $$\frac{24}{5}=\frac{9}{y+2}$$

Simplify the expression if possible. $$\frac{x^{3}+9 x^{2}+14 x}{x^{2}-4}$$

Solve the percent problem. \(\$ 4\) is \(2.5 \%\) of what amount?

Divide. Divide \(16 y^{3}-36 y^{2}-64\) by \(-4 y^{2}\).

Simplify the expression. $$\frac{x}{x+2} \div \frac{x+5}{x+2}$$

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=3, y=7$$

Simplify the expression. $$\frac{x}{x-10}+\frac{x+4}{x+6}$$

Solve the equation by multiplying each side by the least common denominator. $$\frac{1}{x-4}+\frac{1}{x+4}=\frac{22}{x^{2}-16}$$

Solve the proportion. Check for extraneous solutions. $$\frac{6}{3}=\frac{x+8}{-1}$$

Simplify the expression if possible. $$\frac{x^{3}-x}{x^{3}+5 x^{2}-6 x}$$

Solve the percent problem. 33 grams is \(22 \%\) of what weight?

Simplify the expression. $$\frac{5 x+15}{3 x} \div \frac{x+3}{9 x}$$

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=16, y=1$$

Simplify the expression. $$\frac{4 x}{5 x-2}-\frac{2 x}{5 x+1}$$

Solve the equation by multiplying each side by the least common denominator. $$\frac{1}{x-4}+1=-\frac{7}{x^{2}+x-20}$$

Solve the proportion. Check for extraneous solutions. $$\frac{r+4}{3}=\frac{r}{5}$$

For what values of the variable is the rational expression undefined? $$\frac{7}{x-3}$$

Solve the percent problem. 55 years is what percent of 20 years?

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=11, y=2$$

Simplify the expression. $$\frac{2(x+2)}{5(x-3)} \div \frac{4(x-2)}{5 x-15}$$

Simplify the expression. $$\frac{x+8}{3 x-1}+\frac{x+3}{x+1}$$

Solve the equation by multiplying each side by the least common denominator. $$2+\frac{8}{x-5}=\frac{x+5}{x^{2}-25}$$

Solve the proportion. Check for extraneous solutions. $$\frac{w+4}{2 w}=\frac{-5}{6}$$

For what values of the variable is the rational expression undefined? $$\frac{11}{x-8}$$

Match the polynomial division problem with the correct answer. A. \(6+\frac{13}{2 x-3}\) B. \(5 x+4\) C. \(2 x+1\) D. \(5 x-8+\frac{19}{x+2}\) $$\left(10 x^{2}-7 x-12\right) \div(2 x-3)$$

Solve the percent problem. How much is \(8.2 \%\) of 800 tons?

Simplify the expression. $$\frac{x^{2}-36}{-5 x^{2}} \div(x-6)$$

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=\frac{1}{2}, y=8$$

Simplify the expression. $$\frac{3 x+10}{7 x-4}-\frac{x}{4 x+3}$$

Solve the equation. $$\frac{1}{4}+\frac{4}{x}=\frac{1}{x}$$

Solve the proportion. Check for extraneous solutions. $$\frac{5}{2 y}=\frac{7}{y-3}$$

For what values of the variable is the rational expression undefined? $$\frac{4}{x^{2}-1}$$

Solve the percent problem. 9 people is what percent of 60 people?

Simplify the expression. $$\frac{8}{2+3 x} \cdot(8+12 x)$$

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=\frac{13}{5}, y=5$$

Simplify the expression. $$\frac{2 x+1}{3 x-1}-\frac{x+4}{x-2}$$

Solve the equation. $$\frac{-3 x}{x+1}=\frac{-2}{x-1}$$

Solve the proportion. Check for extraneous solutions. $$\frac{x+6}{3}=\frac{x-5}{2}$$

For what values of the variable is the rational expression undefined? $$\frac{x+3}{x^{2}-9}$$

Divide. Divide \(a^{2}-3 a+2\) by \(a-1\)

Solve the percent problem. 62 hours is what percent of 3 days?

Simplify the expression. $$\frac{3 x}{x^{2}-2 x-24} \cdot \frac{x-6}{6 x^{2}+9 x}$$

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=12, y=\frac{3}{4}$$

Simplify the expression. $$\frac{x}{x^{2}+5 x-24}+\frac{8}{x^{2}+5 x-24}$$

Solve the equation. $$\frac{1}{5}-\frac{2}{5 x}=\frac{1}{x}$$

Solve the proportion. Check for extraneous solutions. $$\frac{x-2}{4}=\frac{x+10}{10}$$

For what values of the variable is the rational expression undefined? $$\frac{x+9}{x^{2}+x-12}$$

Divide. Divide \(y^{2}+5 y+7\) by \(y+2\)