Chapter 6

Simplify each complex fraction. $$\frac{\frac{1}{a-b}-\frac{3}{a+b}}{\frac{2}{b-a}+\frac{4}{b+a}}$$

Find the solution set to each equation. $$\frac{x}{5}=\frac{x+2}{3}$$

Simplify each complex fraction. $$\frac{\frac{3}{2+x}-\frac{4}{2-x}}{\frac{1}{x+2}-\frac{3}{x-2}}$$

Reduce each rational expression to its lowest terms. $$\frac{b^{8}-a b^{5}}{a b^{5}}$$

Find the solution set to each equation. $$\frac{2}{x+1}=\frac{x-1}{4}$$

Solve each problem. Patrick drives 40 miles to work, and Guy drives 60 miles to work. Guy claims that he drives at the same speed as Patrick, but it takes him only 12 minutes longer to get to work. If this is true, then how long does it take each of them to get to work? What are their speeds? Do you think that Guy's claim is correct?

Simplify each complex fraction. $$\frac{\frac{4}{y}-\frac{y+4}{y-3}}{\frac{2}{y-3}+\frac{y+1}{y}}$$

Reduce each rational expression to its lowest terms. $$\frac{a-b}{2 b-2 a}$$

Find the solution set to each equation. $$\frac{3}{x-2}=\frac{x+2}{7}$$

Solve each problem. David and Keith are route drivers for a fast-photo company. David's route is 80 miles, and Keith's is 100 miles. Keith averages 10 mph more than David and finishes his route 10 minutes before David. What is David's speed?

Simplify each complex fraction. $$\frac{\frac{x+4}{x+1}+\frac{4}{x}}{\frac{x+1}{x}-\frac{1}{x+1}}$$

Reduce each rational expression to its lowest terms. $$\frac{2 m-2 n}{4 n-4 m}$$

Find the solution set to each equation. $$\frac{x}{6}=\frac{5}{x-1}$$

Solve each problem. Every morning, Yong Yi runs 5 miles, then walks 1 mile. He runs 6 mph faster than he walks. If his total time yesterday was 45 minutes, then how fast did he run?

Simplify each complex fraction. $$\frac{3-\frac{4}{a-1}}{5-\frac{3}{1-a}}$$

Reduce each rational expression to its lowest terms. $$\frac{3 x+6}{3 x}$$

Find the solution set to each equation. $$\frac{x+5}{2}=\frac{3}{x}$$

Solve each problem. Norma can row her boat 12 miles in the same time as it takes Marietta to cover 36 miles in her motorboat. If Marietta's boat travels 15 mph faster than Norma's boat, then how fast is Norma rowing her boat?

Simplify each complex fraction. $$\frac{\frac{x}{3}-\frac{x-1}{9-x}}{\frac{x}{6}-\frac{2-x}{x-9}}$$

Reduce each rational expression to its lowest terms. $$\frac{7 x-14}{7 x}$$

Find the solution set to each equation. $$\frac{x+7}{x+4}=\frac{x+1}{x-2}$$

Solve each problem. A large pump can drain an 80,000 dollars. gallon pool in 3 hours. With a smaller pump also operating, the job takes only 2 hours. How long would it take the smaller pump to drain the pool by itself?

Reduce each rational expression to its lowest terms. $$\frac{a^{3}-b^{3}}{a-b}$$

Find the solution set to each equation. $$\frac{x+1}{x-5}=\frac{x+2}{x-4}$$

Solve each problem. Lourdes can trim the hedges around her property in 8 hours by using an electric hedge trimmer. Rafael can do the same job in 15 hours by using a manual trimmer. How long would it take them to trim the hedges working together?

Simplify each complex fraction. $$\frac{\frac{1}{y+2}-\frac{4}{3 y}}{\frac{3}{y}-\frac{2}{y+3}}$$

Reduce each rational expression to its lowest terms. $$\frac{27 x^{3}+y^{3}}{6 x+2 y}$$

Find the solution set to each equation. $$\frac{x-2}{x-3}=\frac{x+5}{x+2}$$

Perform the indicated operations. Reduce answers to lowest terms. See Examples \(3-5\) $$ \frac{7}{48}-\frac{5}{36} $$

Simplify each complex fraction. $$\frac{\frac{3}{x^{2}-1}-\frac{x-2}{x^{3}-1}}{\frac{3}{x^{2}+x+1}+\frac{x-3}{x^{3}-1}}$$

Reduce each rational expression to its lowest terms. $$\frac{4 x^{2}-4}{4 x^{2}+4}$$

Find the solution set to each equation. $$\frac{a-5}{a+6}=\frac{a-7}{a+8}$$

Solve each problem. Charles can empty the cookie jar in \(1 \frac{1}{2}\) hours. It takes his mother 2 hours to bake enough cookies to fill it. If the cookie jar is full when Charles comes home from school, and his mother continues baking and restocking the cookie jar, then how long will it take him to empty the cookie jar?

Simplify each complex fraction. $$\frac{\frac{2}{a^{3}+8}-\frac{3}{a^{2}-2 a+4}}{\frac{4}{a^{2}-4}+\frac{a-3}{a^{3}+8}}$$

Reduce each rational expression to its lowest terms. $$\frac{2 a^{2}-2 b^{2}}{2 a^{2}+2 b^{2}}$$

Find the solution set to each equation. $$\frac{3 w}{3 w-5}=\frac{w}{w+2}$$

Solve each problem. It takes Gina 90 minutes to file the monthly invoices. If Hilda files twice as fast as Gina does, how long will it take them working together?

Simplify. $$\frac{w^{-1}+y^{-1}}{z^{-1}+y^{-1}}$$

Reduce each rational expression to its lowest terms.. $$\frac{12 x^{2}-26 x-10}{4 x^{2}-25}$$

Solve each problem. Painting alone. Julie can paint a fence by herself in 12 hours. With Betsy's help, it takes only 5 hours. How long would it take Betsy by herself?

Simplify. $$\frac{a^{-1}-b^{-1}}{a^{-1}+b^{-1}}$$

Reduce each rational expression to its lowest terms. $$\frac{9 x^{2}-15 x-6}{81 x^{2}-9}$$

Solve each equation. $$\frac{a}{9}=\frac{4}{a}$$

Solve each problem. Molly bought 5.28 dollars worth of oranges and 8.80 dollars worth of apples. She bought 2 more pounds of oranges than apples. If apples cost twice as much per pound as oranges, then how many pounds of each did she buy?

Simplify. $$\frac{1-x^{-1}}{1-x^{-2}}$$

Reduce each rational expression to its lowest terms. $$\frac{x^{3}+7 x^{2}-4 x}{x^{3}-16 x}$$

Solve each equation. $$\frac{y}{3}=\frac{27}{y}$$

Simplify. $$\frac{4-a^{-2}}{2-a^{-1}}$$

Reduce each rational expression to its lowest terms. $$\frac{2 x^{4}-32}{4 x-8}$$

Solve each equation. $$\frac{x}{9}=\frac{-20}{9 x}+1$$