91Ó°ÊÓ

For Exercises 1 and \(2,\) determine whether the statement is true or false. Literal equations are solved using the same properties of equations that are used to solve equations in one variable.

Determine whether the statement is true or false. To add two fractions, add the numerators and the denominators.

Fill in the blank to make a true statement. If it takes a janitorial crew \(5 \mathrm{h}\) to clean a company's offices, then in \(x\) hours the crew has completed ______ of the job.

Determine whether the statement is true or false. To simplify a complex fraction, multiply the complex fraction by the LCM of the denominators of the fractions in the numerator and denominator of the complex fraction.

Determine whether the statement is true or false. Our goal in simplifying a complex fraction is to rewrite it so that there are no fractions in the numerator or in the denominator. We then express the fraction in simplest form.

Simplify. $$\frac{1+\frac{3}{x}}{1-\frac{9}{x^{2}}}$$

The speed of a plane is 500 mph. There is a headwind of 50 mph. What is the speed of the plane relative to an observer on the ground?

It takes Doug 6 days to reroof a house. If Doug's son helps him, the job can be completed in 4 days. How long would it take Doug's son, working alone, to do the job?

Find the LCM of the polynomials. $$\begin{aligned} &x^{2}+3 x-10\\\ &x^{2}+5 x-14 \end{aligned}$$

Two welders working together can complete a job in 6 h. One of the welders, working alone, can complete the task in 10 h. How long would it take the second welder, working alone, to complete the task?