91Ó°ÊÓ

Perform the indicated operations. Simplify when possible $$ \frac{2 y-6}{y^{2}-9}-\frac{y}{y-1}+\frac{y^{2}+2}{y^{2}+2 y-3} $$

Divide and, if possible, simplify. $$ \frac{5 y-5 x}{15 y^{3}} \div \frac{x^{2}-y^{2}}{3 x+3 y} $$

A rational function \(f\) is given. Find all values of a for which \(f(a)\) is the indicated value. $$ f(x)=\frac{x-5}{x+1} ; f(a)=\frac{3}{5} $$

The printer in an admissions office can print a 500 -page document in 5 min, while the printer in the business office can print the same document in 4 min. If the two printers work together to print the document, with the faster machine starting on page 1 and the slower machine working backwards from page \(500,\) at what page will the two machines meet to complete the job?

Simplify. If possible, use a second method or evaluation as a check. Parker incorrectly simplifies $$ \frac{a+b^{-1}}{a+c^{-1}} \text { as } \frac{a+c}{a+b} $$ What mistake is he probably making and how could you convince him that this is incorrect?

At what time after 4: 00 will the minute hand and the hour hand of a clock first be in the same position?

Divide. Find \(k\) such that when \(x^{3}-k x^{2}+3 x+7 k\) is divided by \(x+2,\) the remainder is \(0 .\)

A rational function \(f\) is given. Find all values of a for which \(f(a)\) is the indicated value. $$ f(x)=\frac{x-3}{x+2} ; f(a)=\frac{1}{5} $$

Perform the indicated operations. Simplify when possible $$ \frac{x-1}{x^{2}-1}-\frac{x}{x-2}+\frac{x^{2}+2}{x^{2}-x-2} $$

The wavelength \(W\) of a radio wave varies inversely as its frequency \(F\) A wave with a frequency of 1200 kilohertz has a length of 300 meters. What is the length of a wave with a frequency of 800 kilohertz?