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Chapter 7: Problem 18
Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{y+7}{y^{2}-49}$$
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denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x^{2}}{x-3}+\frac{9}{3-x}$$
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?
denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{4-x}{x-9}-\frac{3 x-8}{9-x}$$
perform the indicated operations. Simplify the result, if possible. $$\left(\frac{3 x-1}{x^{2}+5 x-6}-\frac{2 x-7}{x^{2}+5 x-6}\right) \div \frac{x+2}{x^{2}-1}$$
denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{y}{y-4}-\frac{4}{4-y}$$
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