Chapter 6

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{x^{2}+3 x-3}{x-4}-\frac{x^{2}+4 x-7}{x-4} $$

Which real numbers cannot be used in place of the variable in each rational expression? $$\frac{3 b+1}{b^{2}-3 b-4}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}} \text { for } T_{1}$$

Find the solution set to each equation. $$\frac{3 x-5}{x-1}=2-\frac{2 x}{x-1}$$

Perform the indicated operations. Reduce answers to their lowest terms. See Example \(I\) $$ \frac{2 x^{2}-8 x-4}{2 x^{2}+7 x+3}+\frac{4 x^{2}+x-1}{2 x^{2}+7 x+3} $$

Which real numbers cannot be used in place of the variable in each rational expression? $$\frac{x+1}{x^{3}+x^{2}-6 x}$$

$$\text { Solve each formula for the indicated variable.}$$ $$\frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}} \text { for } P_{2}$$

Find the solution set to each equation. $$\frac{x-3}{x+2}=3-\frac{1-2 x}{x+2}$$

Which real numbers cannot be used in place of the variable in each rational expression? $$\frac{x^{2}-3 x-4}{2 x^{5}-2 x}$$

$$\text { Solve each formula for the indicated variable.}$$ $$V=\frac{4}{3} \pi r^{2} h \text { for } h$$

Find the solution set to each equation. $$x+1+\frac{2 x-5}{x-5}=\frac{x}{x-5}$$

Reduce each rational expression to its lowest terms. $$\frac{6}{57}$$

$$\text { Solve each formula for the indicated variable.}$$ $$h=\frac{S-2 \pi r^{2}}{2 \pi r} \text { for } S$$

Find the solution set to each equation. $$\frac{x-3}{2}-\frac{1}{x-3}=\frac{8-3 x}{x-3}$$

Reduce each rational expression to its lowest terms. $$\frac{14}{91}$$

Find the solution set to each equation. $$5+\frac{9}{x-2}=2+\frac{x+7}{x-2}$$

Find the value of the indicated variable. Round approximate answers to three decimal places. Find \(f\) if \(M=10, F=5,\) and \(M=\frac{F}{f}\)

Reduce each rational expression to its lowest terms. $$\frac{42}{210}$$

Find the solution set to each equation. $$3+\frac{x+1}{x-3}=2-\frac{5-3 x}{x-3}$$

Find the value of the indicated variable. Round approximate answers to three decimal places. $$\text { Find } r \text { if } A=550, P=500, t=2, \text { and } P=\frac{A}{1+r t}$$

Reduce each rational expression to its lowest terms. $$\frac{242}{154}$$

Find the solution set to each equation. $$\frac{2}{x+2}+\frac{x}{x-3}+\frac{1}{x^{2}-x-6}=0$$

Find the value of the indicated variable. Round approximate answers to three decimal places. Find \(h\) if \(r=3, V=12 \pi,\) and \(r^{2}=\frac{V}{\pi h}\)

Simplify each complex fraction. $$\frac{x+\frac{4}{x+4}}{x-\frac{4 x+4}{x+4}}$$

Reduce each rational expression to its lowest terms. $$\frac{2 x+2}{4}$$

Find the solution set to each equation. $$\frac{x-4}{x^{2}+2 x-15}=2-\frac{2}{x-3}$$

Find the value of the indicated variable. Round approximate answers to three decimal places. $$\text { Find } k \text { if } F=32, r=4, m_{1}=6, m_{2}=8, \text { and } m_{1}=\frac{F r^{2}}{km_{2}}$$

Simplify each complex fraction. $$\frac{x-\frac{x+6}{x+2}}{x-\frac{4 x+15}{x+2}}$$

Reduce each rational expression to its lowest terms. $$\frac{3 a+3}{3}$$

Find the solution set to each equation. $$\frac{2}{x}=\frac{3}{4}$$

Find the value of the indicated variable. Round approximate answers to three decimal places. $$\text { Find } r \text { if } F=10, m=8, v=6, \text { and } F=\frac{m v^{2}}{r}$$

Simplify each complex fraction. $$\frac{1-\frac{1}{y-1}}{3+\frac{1}{y+1}}$$

Reduce each rational expression to its lowest terms. $$\frac{3 x-6 y}{10 y-5 x}$$

Find the solution set to each equation. $$\frac{5}{x}=\frac{7}{9}$$

Find the value of the indicated variable. Round approximate answers to three decimal places. $$\text { Find } p \text { if } f=2.3, q=1.7, \text { and } \frac{1}{p}+\frac{1}{q}=\frac{1}{f}$$

Simplify each complex fraction. $$\frac{2-\frac{3}{a-2}}{4-\frac{1}{a+2}}$$

Find the solution set to each equation. $$\frac{a}{3}=\frac{-1}{4}$$

Simplify each complex fraction. $$\frac{\frac{2}{3-x}-4}{\frac{1}{x-3}-1}$$

Reduce each rational expression to its lowest terms. $$\frac{a b^{2}}{a^{3} b}$$

Find the solution set to each equation. $$\frac{b}{5}=\frac{-3}{7}$$

Simplify each complex fraction. $$\frac{\frac{x}{x-5}-2}{\frac{2 x}{5-x}-1}$$

Reduce each rational expression to its lowest terms. $$\frac{36 y^{3} z^{8}}{54 y^{2} z^{9}}$$

Find the solution set to each equation. $$-\frac{5}{7}=\frac{2}{x}$$

Solve each problem. Karen can ride her bike from home to school in the same amount of time as she can walk from home to the post office. She rides 10 miles per hour (mph) faster than she walks. The distance from her home to school is 7 miles, and the distance from her home to the post office is 2 miles. How fast does Karen walk? (IMAGE CAN'T COPY)

Simplify each complex fraction. $$\frac{\frac{w+2}{w-1}-\frac{w-3}{w}}{\frac{w+4}{w}+\frac{w-2}{w-1}}$$

Reduce each rational expression to its lowest terms. $$\frac{-2 w^{2} x^{3} y}{6 w x^{5} y^{2}}$$

Find the solution set to each equation. $$-\frac{3}{8}=\frac{5}{x}$$

Solve each problem. Beverly can drive 600 miles in the same time as it takes Susan to drive 500 miles. If Beverly drives 10 mph faster than Susan, then how fast does Beverly drive?

Reduce each rational expression to its lowest terms. $$\frac{6 a^{3} b^{12} c^{5}}{-8 a b^{4} c^{9}}$$

Find the solution set to each equation. $$\frac{10}{x}=\frac{20}{x+20}$$