Chapter 7

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

Each exercise is a problem involving work. A hurricane strikes and a rural area is without food or water. Three crews arrive. One can dispense needed supplies in 10 hours, a second in 15 hours, and a third in 20 hours. How long will it take all three crews working together to dispense food and water?

A person's salary, \(S\), varies directly as the number of hours worked, \(h\) a. Write an cquation that expresses this relationship. b. For a 40 -hour work week, Gloria earned 1400 dollar. Substitute 1400 for \(S\) and 40 for \(h\) in the equation from part (a) and find \(k,\) the constant of variation. c. Substitute the value of \(k\) into your equation in part (a) and write the equation that describes Gloria's salary in terms of the number of hours she works. d. Use the equation from part (c) to find Gloria's salary for 25 hours of work.

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{x+7}{7}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{y}-\frac{3}{4}}{\frac{1}{y}+\frac{2}{3}}\)

Find the least common denominator of the rational expressions. $$\frac{9}{y^{2}-25} \text { and } \frac{y}{y^{2}-10 y+25}$$

Solve each rational equation. $$\frac{7}{x+1}=\frac{5}{x-3}$$

Multiply as indicated. $$\frac{9 y+21}{y^{2}-2 y} \cdot \frac{y-2}{3 y+7}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x-4}+\frac{9 x+7}{x-4}$$

Each exercise is a problem involving work. A pool can be filled by one pipe in 4 hours and by a second pipe in 6 hours. How long will it take using both pipes to fill the pool?

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{y+3}{4 y^{2}+y-3}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{x}{5}-\frac{5}{x}}{\frac{1}{5}+\frac{1}{x}}\)

Find the least common denominator of the rational expressions. $$\frac{3}{x^{2}-x-20} \text { and } \frac{x}{2 x^{2}+7 x-4}$$

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

Multiply as indicated. $$\frac{y^{2}-7 y-30}{y^{2}-6 y-40} \cdot \frac{2 y^{2}+5 y+2}{2 y^{2}+7 y+3}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{4 x+1}{6 x+5}+\frac{8 x+9}{6 x+5}$$

Each exercise is a problem involving work. A pool can be filled by one pipe in 3 hours and by a second pipe in 6 hours. How long will it take using both pipes to fill the pool?

Use the four-step procedure for solving variation problems given on page 551 An object's weight on the moon, \(M,\) varies directly as its weight on Earth, \(E .\) A person who weighs 55 kilograms on Earth weighs 8.8 kilograms on the moon. What is the moon weight of a person who weighs 90 kilograms on Earth?

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{y+8}{6 y^{2}-y-2}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{3}{x}+\frac{x}{3}}{\frac{x}{3}-\frac{3}{x}}\)

Find the least common denominator of the rational expressions. $$\frac{7}{x^{2}-5 x-6} \text { and } \frac{x}{x^{2}-4 x-5}$$

Solve each rational equation. $$\frac{7 x-4}{5 x}=\frac{9}{5}-\frac{4}{x}$$

Multiply as indicated. $$\frac{3 y^{2}+17 y+10}{3 y^{2}-22 y-16} \cdot \frac{y^{2}-4 y-32}{y^{2}-8 y-48}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{3 x+2}{3 x+4}+\frac{3 x+6}{3 x+4}$$

Use a proportion to solve each problem. The tax on a property with an assessed value of 65,000 dollars is 720 dollars . Find the tax on a property with an assessed value of 162,500 dollars

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{y+5}{y^{2}-25}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{y^{2}+7 y}{y^{2}-5 y}+\frac{y^{2}-4 y}{y^{2}-5 y}$$

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

Solve each rational equation. $$x+\frac{6}{x}=-7$$

Multiply as indicated. $$\left(y^{2}-9\right) \cdot \frac{4}{y-3}$$

Use a proportion to solve each problem. The maintenance bill for a shopping center containing \(180,000\) square feet is $$ 45,000 .$ What is the bill for a store in the center that is 4800 square feet?

Use the four-step procedure for solving variation problems given on page 551 A golf ball's bounce height, \(B\), in inches, varies directly as its drop height, \(d\), in inches. A golf ball bounces 36 inches when dropped from a height of 40 inches. What is the ball's bounce height if the drop height is increased to 50 inches?

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{y+7}{y^{2}-49}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{y^{2}-2 y}{y^{2}+3 y}+\frac{y^{2}+y}{y^{2}+3 y}$$

Simplify complex rational expression by the method of your choice. \(\frac{1+\frac{2}{x}}{1-\frac{4}{x^{2}}}\)

Solve each rational equation. $$x+\frac{7}{x}=-8$$

Multiply as indicated. $$\left(y^{2}-16\right) \cdot \frac{3}{y-4}$$

Use a proportion to solve each problem. St. Paul Island in Alaska has 12 fur seal rookeries (breeding places). In \(1961,\) to estimate the fur seal pup population in the Gorbath rookery, 4963 fur seal pups were tagged in early August. In late August, a sample of 900 pups was observed and 218 of these were found to have been previously tagged. Estimate the total number of fur seal pups in this rookery.

Use the four-step procedure for solving variation problems given on page 551 The time that it takes to get to campus varies inversely as your driving rate. Averaging 20 miles per hour in terrible traffic, it takes you 1.5 hours to get to campus. How long would the trip take averaging 60 miles per hour?

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{5}{x^{2}+1}$$

add or subtract as indicated. Simplify the result, if possible. $$\frac{4 y-1}{5 y^{2}}+\frac{3 y+1}{5 y^{2}}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{7}-\frac{1}{y}}{\frac{7-y}{7}}\)

Multiply as indicated. $$\frac{x^{2}-5 x+6}{x^{2}-2 x-3} \cdot \frac{x^{2}-1}{x^{2}-4}$$

Solve each rational equation. $$\frac{x}{5}-\frac{5}{x}=0$$

Use a proportion to solve each problem. To estimate the number of bass in a lake, wildlife biologists tagged 50 bass and released them in the lake. Later they netted 108 bass and found that 27 of them were tagged. Approximately how many bass are in the lake?

Add or subtract as indicated. Simplify the result, if possible. $$\frac{5}{6 x}+\frac{7}{8 x}$$

Use the four-step procedure for solving variation problems given on page 551 The weight that can be supported by a 2 -inch by 4 -inch picce of pine (called a 2 -by-4) varies inversely as its length. A 10 -foot 2 -by- 4 can support 500 pounds. What weight can be supported by a 5 -foot 2 -by- \(4 ?\)

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{8}{x^{2}+4}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{1}{9}-\frac{1}{y}}{\frac{9-y}{9}}\)

Multiply as indicated. $$\frac{x^{2}+5 x+6}{x^{2}+x-6} \cdot \frac{x^{2}-9}{x^{2}-x-6}$$