91Ó°ÊÓ

Divide as indicated. $$\left(y^{2}-16\right) \div \frac{y^{2}+3 y-4}{y^{2}+4}$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{2 x+3}{2 x+5}$$

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

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3 y}{4 y-20}+\frac{9 y}{6 y-30}$$

Make Sense? In Exercises \(42-45,\) determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can clean my house in 3 hours and my sloppy friend can completely mess it up in 6 hours, so if we both "work" together, the time, \(x,\) it takes to clean the house can be modeled by \(\frac{x}{3}-\frac{x}{6}=1\)

Add or subtract as indicated. Simplify the result, if possible. $$\frac{4 y}{5 y-10}+\frac{3 y}{10 y-20}$$

Two skiers begin skiing along a trail at the same time. The faster skier averages 9 miles per hour and the slower skier averages 6 miles per hour. The faster skier completes the trail \(\frac{1}{4}\) hour before the slower skier. How long is the trail?

In Exercises \(1-46,\) solve each rational equation. $$\frac{x-3}{x-2}+\frac{x+1}{x+3}=\frac{2 x^{2}-15}{x^{2}+x-6}$$

Denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-3}+\frac{9}{3-x}$$

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3 x+7}{3 x+10}$$