Chapter 11

Solve the equation. Remember to check for extraneous solutions. $$\frac{4}{x^{2}-2 x}=\frac{4}{3 x-6}$$

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

Simplify the expression if possible. $$\frac{4 x}{20}$$

Divide. Divide 856 by 29

Solve the percent problem. The price of a book without tax is \(\$ 5.99\) and the sales tax rate is \(6 \% .\) Find the amount of the tax by using an equation of the form \(a=p b\) and by using a proportion. How are the two methods similar?

Simplify the expression. $$\frac{4 x^{2}-25}{4 x} \div(2 x-5)$$

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

Solve the equation. Remember to check for extraneous solutions. $$\frac{4}{x(x+1)}=\frac{3}{x}$$

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

Simplify the expression if possible. $$\frac{15 x}{45}$$

Divide. Divide \(18 x^{2}+45 x-36\) by \(9 x\)

Match the percent problem with the equation that represents it. 39 is \(50 \%\) of what number?

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

When \(x=4, y=6 .\) For the given type of variation, find an equation that relates \(x\) and \(y .\) Then find the value of \(y\) when \(x=8\). \(x\) and \(y\) vary directly.

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

Solve the equation. Remember to check for extraneous solutions. $$\frac{3}{x+4}+\frac{4}{x}=\frac{-5}{x^{2}+4 x}$$

Solve the proportion. Check for extraneous solutions. $$\frac{2}{2 x+1}=\frac{1}{5}$$

Simplify the expression if possible. $$\frac{-18 x^{2}}{12 x}$$

Divide. Divide \(x^{2}-8 x+15\) by \(x-3\)

Match the percent problem with the equation that represents it. A. \(a=(0.39)(50)\) B. \(39=p(50)\) C. \(39=0.50 b\) \(39 \%\) of 50 is what number?

Simplify the expression. $$\frac{9 x^{2}+6 x+1}{x+5} \div \frac{3 x+1}{x^{2}+5 x}$$

When \(x=4, y=6 .\) For the given type of variation, find an equation that relates \(x\) and \(y .\) Then find the value of \(y\) when \(x=8\). \(x\) and \(y\) vary inversely.

Simplify the expression. $$\frac{7 x}{x^{3}}-\frac{6 x}{x^{3}}$$

Find the center of the hyperbola. Draw the asymptotes and sketch the graph. $$y=\frac{4}{x+5}-3$$

Solve the proportion. Check for extraneous solutions. $$\frac{3}{x}=\frac{x+1}{4}$$

Simplify the expression if possible. $$\frac{14 x^{2}}{50 x^{4}}$$

Divide. Divide \(y^{2}+6 y+2\) by \(y+3\)

Match the percent problem with the equation that represents it. A. \(a=(0.39)(50)\) B. \(39=p(50)\) C. \(39=0.50 b\) \(\$ 39\) is what percent of \(\$ 50 ?\)

Simplify the expression. $$\frac{4 x}{3} \cdot \frac{1}{x}$$

The variables x and y vary directly. Use the given values to write an equation that relates x and y. $$x=3, y=9$$

Simplify the expression. $$\frac{2}{3 x-1}-\frac{5 x}{3 x-1}$$

Find the center of the hyperbola. Draw the asymptotes and sketch the graph. $$y=\frac{2}{x-2}+3$$

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

Simplify the expression if possible. $$\frac{3 x^{2}-18 x}{-9 x^{2}}$$

Divide. Divide \(10 b^{3}-8 b^{2}-5 b\) by \(-2 b\)

Solve the percent problem. What number is \(25 \%\) of \(80 ?\)

Simplify the expression. $$\frac{9 x^{2}}{4} \cdot \frac{8}{18 x}$$

The variables x and y vary directly. Use the given values to write an equation that relates x and y. $$x=2, y=8$$

Simplify the expression. $$\frac{3 x}{4 x+1}+\frac{5 x}{4 x+1}$$

Solve the equation by cross multiplying. $$\frac{x}{5}=\frac{7}{3}$$

Solve the proportion. Check for extraneous solutions. $$\frac{2 u-3}{4 u}=\frac{u-1}{u}$$

Simplify the expression if possible. $$\frac{42 x-6 x^{3}}{36 x}$$

Divide. Divide \(2 x^{2}-x+4\) by \(3 x-6\)

Solve the percent problem. \(85 \%\) of 300 is what number?

Simplify the expression. $$\frac{7 x^{2}}{6 x} \cdot \frac{12 x^{2}}{2 x}$$

The variables x and y vary directly. Use the given values to write an equation that relates x and y. $$x=18, y=6$$

Simplify the expression. $$\frac{-8}{3 x^{2}}+\frac{11}{3 x^{2}}$$

Solve the equation by cross multiplying. $$\frac{x}{10}=\frac{14}{5}$$

Simplify the expression if possible. $$\frac{7 x}{12 x+x^{2}}$$

Divide. Divide \(8 x+13\) by 2.