91Ó°ÊÓ

Add or subtract as indicated. Write all answers in lowest terms. $$ \frac{5}{x}+\frac{9}{4 x} $$

Write each rational expression in lowest terms. $$ \frac{a^{3}+b^{3}}{a+b} $$

Solve each problem. See Examples \(1-7\) Over a specified distance, rate varies inversely with time. If a Dodge Viper on a test track goes a certain distance in one-half minute at 160 mph, what rate is needed to go the same distance in three-fourths minute?

Add or subtract as indicated. Write all answers in lowest terms. $$ \frac{5}{12 x^{2} y}-\frac{11}{6 x y} $$

Write each rational expression in lowest terms. $$ \frac{r^{3}-s^{3}}{r-s} $$

Add or subtract as indicated. Write all answers in lowest terms. $$ \frac{7}{18 a^{3} b^{2}}-\frac{2}{9 a b} $$

For each rational function, find all numbers that are not in the domain. Then give the domain, using set-builder notation. See Section 7.1. $$ f(x)=\frac{1}{x^{2}-16} $$

Solve each problem. See Examples \(1-7\) For a constant area, the length of a rectangle varies inversely as the width. The length of a rectangle is 27 ft when the width is 10 ft. Find the width of a rectangle with the same area if the length is \(18 \mathrm{ft}\).

Write each rational expression in lowest terms. $$ \frac{2 c^{2}+2 c d-60 d^{2}}{2 c^{2}-12 c d+10 d^{2}} $$

Solve each problem. See Examples \(1-7\) The frequency of a vibrating string varies inversely as its length. That is, a longer string vibrates fewer times in a second than a shorter string. Suppose a piano string 2 ft long vibrates 250 cycles per sec. What frequency would a string 5 ft long have?