Chapter 7

Multiply as indicated. $$\frac{2 y}{3 y-y^{2}} \cdot \frac{2 y^{2}-9 y+9}{8 y-12}$$

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

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

Explain the meaning of this statement: A company's monthly sales vary inversely as the price of its product.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{-15}{3 x-9}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{12}{x^{2}}-\frac{3}{x}}{\frac{15}{x}-\frac{9}{x^{2}}}\)

Multiply as indicated.$ $$\frac{x^{2}-y^{2}}{x} \cdot \frac{x^{2}+x y}{x+y}$$

Solve each rational equation. $$\frac{1}{x-1}+5=\frac{11}{x-1}$$

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

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. The time it takes me to drive to campus varies directly as my rate of travel.

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{-21}{7 x-14}$$

Simplify complex rational expression by the method of your choice. \(\frac{\frac{8}{x^{2}}-\frac{2}{x}}{\frac{10}{x}-\frac{6}{x^{2}}}\)

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

Solve each rational equation. $$\frac{3}{x+4}-7=\frac{-4}{x+4}$$

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

Use similar triangles to solve. A tree casts a shadow 12 feet long. At the same time, a vertical rod 8 feet high casts a shadow 6 feet long. How tall is the tree? (IMAGE CANNOT COPY)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. It seems reasonable that a student's grade in a course varies directly as the number of hours spent studying.

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

Simplify complex rational expression by the method of your choice. \(\frac{2+\frac{6}{y}}{1-\frac{9}{y^{2}}}\)

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

Solve each rational equation. $$\frac{8 y}{y+1}=4-\frac{8}{y+1}$$

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

Use similar triangles to solve. A person who is 5 feet tall is standing 80 feet from the base of a tree. The tree casts an 86 -foot shadow. The person's shadow is 6 feet in length. What is the tree's height? (IMAGE CANNOT COPY)

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{5 x-10}{x-2}$$

Simplify complex rational expression by the method of your choice. \(\frac{3+\frac{12}{y}}{1-\frac{16}{y^{2}}}\)

Multiply as indicated.$ $$\frac{x^{2}-y^{2}}{x+y} \cdot \frac{x+2 y}{2 x^{2}-x y-y^{2}}$$

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

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

What is the relationship among time traveled, distance traveled, and rate of travel?

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x+5}{x^{2}-25}$$

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

Divide as indicated. $$\frac{x}{7}+\frac{5}{3}$$

Solve each rational equation. $$\frac{3}{x-1}+\frac{8}{x}=3$$

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

If you know how many hours it takes for you to do a job, explain how to find the fractional part of the job you can complete in \(x\) hours.

The intensity of radiation from a machine used to treat tumors varies inversely as the square of the distance from the machine. If the intensity is 140.5 milliroentgens per hour at 2 meters, what is the intensity at a distance of 3 meters?

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{x+4}{x^{2}-16}$$

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

Divide as indicated. $$\frac{x}{3} \div \frac{3}{8}$$

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

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x+7}-1$$

If you can do a job in 6 hours and your friend can do the same job in 3 hours, explain how to find how long it takes to complete the job working together. It is not necessary to solve the problem.

Solve: $$8(2-x)=-5 x$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 y-10}{3 y-15}$$

Simplify complex rational expression by the method of your choice. \(\frac{x-5+\frac{3}{x}}{x-7+\frac{2}{x}}\)

Divide as indicated. $$\frac{3}{x} \div \frac{12}{x}$$

Solve each rational equation. $$\frac{3 y}{y-4}-5=\frac{12}{y-4}$$

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

When two people work together to complete a job, describe one factor that can result in more or less time than the time given by the rational equations we have been using.

Divide: $$\frac{27 x^{3}-8}{3 x+2}$$