Chapter 7

Solve each rational equation. $$\frac{x}{4}-\frac{4}{x}=0$$

Use a proportion to solve each problem. According to the authors of Number Freaking, in a global village of 200 people, 28 suffer from malnutrition. How many people of the world's 6.9 billion people \((2010\) population) suffer from malnutrition? Round to the nearest hundredth of a billion.

Add or subtract as indicated. Simplify the result, if possible. $$\frac{4}{x}+\frac{7}{2 x^{2}}$$

Use the four-step procedure for solving variation problems given on page 551 The volume of a gas in a container at a constant temperature varies inversely as the pressure. If the volume is 32 cubic centimeters at a pressure of 8 pounds per square centimeter, find the pressure when the volume is 40 cubic centimeters.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{14 x^{2}}{7 x}$$

Simplify complex rational expression by the method of your choice. \(\frac{x+\frac{2}{y}}{\frac{x}{y}}\)

$$\frac{x^{2}+5 x+6}{x^{2}+x-6} \cdot \frac{x^{2}-9}{x^{2}-x-6}$$

Solve each rational equation. $$x+\frac{3}{x}=\frac{12}{x}$$

Use a proportion to solve each problem. According to the authors of Number Freaking, in a global village of 200 people, 9 get drunk every day. How many of the world's 6.9 billion people \((2010\) population) get drunk everyday? Round to the nearest hundredth of a billion.

Add or subtract as indicated. Simplify the result, if possible. $$\frac{10}{x}+\frac{3}{5 x^{2}}$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{9 x^{2}}{6 x}$$

Simplify complex rational expression by the method of your choice. \(\frac{x-\frac{2}{y}}{\frac{x}{y}}\)

Multiply as indicated. $$\frac{x^{3}-8}{x^{2}-4} \cdot \frac{x+2}{3 x}$$

Solve each rational equation. $$x+\frac{3}{x}=\frac{19}{x}$$

Use a proportion to solve each problem. Height is proportional to foot length. A person whose foot length is 10 inches is 67 inches tall. In 1951 , photos of large footprints were published. Some believed that these footprints were made by the "Abominable Snowman." Each footprint was 23 inches long. If indeed they belonged to the Abominable Snowman, how tall is the critter? (IMAGE CANNOT COPY)

Add or subtract as indicated. Simplify the result, if possible. $$6+\frac{1}{x}$$

Use the four-step procedure for solving variation problems given on page 551 The number of pens sold varies inversely as the price per pen. If 4000 pens are sold at a price of 1.50 dollar each, find the number of pens sold at a price of 1.20 dollar each.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{5 x-15}{25}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{x}+\frac{1}{y}}{x y}\)

Multiply as indicated. $$\frac{x^{2}+6 x+9}{x^{3}+27} \cdot \frac{1}{x+3}$$

Solve each rational equation. $$\frac{4}{y}-\frac{y}{2}=\frac{7}{2}$$

Use a proportion to solve each problem. A person's hair length is proportional to the number of years it has been growing. After 2 years, a person's hair grows 8 inches. The longest moustache on record was grown by Kalyan Sain of India. Sain grew his moustache for 17 years. How long was each side of the moustache?

add or subtract as indicated. Simplify the result, if possible. $$\begin{aligned} &\frac{x^{2}+9 x}{4 x^{2}-11 x-3}+\frac{3 x-5 x^{2}}{4 x^{2}-11 x-3}\\\ &x^{2}-4 x-4 x-4 \end{aligned}$$

Use the four-step procedure for solving variation problems given on page 551 The time required to accomplish a task varies inversely as the number of people working on the task. It takes 6 hours for 20 people to put a new roof on a porch. How long would it take 30 people to do the job?

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{7 x+21}{49}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{x}+\frac{1}{y}}{x+y}\)

Multiply as indicated. $$\frac{(x+4)^{3}}{(x+2)^{3}} \cdot \frac{x^{2}+4 x+4}{x^{2}+8 x+16}$$

Solve each rational equation. $$\frac{4}{3 y}-\frac{1}{3}=y$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{x}+9$$

What does it mean if two quantities vary directly?

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 x-8}{4 x}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{x}{y}+\frac{1}{x}}{\frac{y}{x}+\frac{1}{x}}\)

Multiply as indicated. $$\frac{6 x+2}{x^{2}-1} \cdot \frac{1-x}{3 x^{2}+x}$$

Solve each rational equation. $$\frac{x-4}{x}=\frac{15}{x+4}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{7}{x}+4$$

In your own words, explain how to solve a variation problem.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3 x-9}{6 x}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{x}+\frac{1}{y}}{\frac{1}{x}-\frac{1}{y}}\)

Multiply as indicated. $$\frac{8 x+2}{x^{2}-9} \cdot \frac{3-x}{4 x^{2}+x}$$

Solve each rational equation. $$\frac{x-1}{2 x+3}=\frac{6}{x-2}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-1}{6}+\frac{x+2}{3}$$

What does it mean if two quantities vary inversely?

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3}{3 x-9}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{y}+\frac{2}{y^{2}}}{\frac{2}{y}+1}\)

Multiply as indicated. $$\frac{25-y^{2}}{y^{2}-2 y-35} \cdot \frac{y^{2}-8 y-20}{y^{2}-3 y-10}$$

Solve each rational equation. $$\frac{2}{x^{2}-1}=\frac{4}{x+1}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x+3}{2}+\frac{x+5}{4}$$

Explain the meaning of this statement: A company's monthly sales vary directly as its advertising budget.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{12}{6 x-18}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{y}+\frac{3}{y^{2}}}{\frac{3}{y}+1}\)