Chapter 4

Perform the indicated divisions. $$ \left(2 x^{3}+x^{2}-3 x+1\right) \div\left(x^{2}+x-1\right) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{t+3}{3 t-1}+\frac{8 t^{2}+8 t+2}{3 t^{2}-7 t+2}-\frac{2 t+3}{t-2} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{3}{n^{2}}-\frac{2}{5 n}+\frac{4}{3} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{3 x^{2}-20 x+25}{2 x^{2}-7 x-15} \div \frac{9 x^{2}-3 x-20}{12 x^{2}+28 x+15}\)

For Problems 9-50, simplify each rational expression. \(\frac{15 x^{3}-15 x^{2}}{5 x^{3}+5 x}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ y=-\frac{a}{b} x+\frac{c}{d} \text { for } x $$

For Problems \(1-44\), solve each equation. $$ \frac{n}{n+1}+\frac{1}{2}=\frac{-2}{n+2} $$

Perform the indicated divisions. $$ \left(3 x^{3}-4 x^{2}+8 x+8\right) \div\left(x^{2}-2 x+4\right) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{t-3}{2 t+1}+\frac{2 t^{2}+19 t-46}{2 t^{2}-9 t-5}-\frac{t+4}{t-5} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{1}{n^{2}}+\frac{3}{4 n}-\frac{5}{6} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{21 t^{2}+t-2}{2 t^{2}-17 t-9} \div \frac{12 t^{2}-5 t-3}{8 t^{2}-2 t-3}\)

For Problems 9-50, simplify each rational expression. \(\frac{5 n^{2}+18 n-8}{3 n^{2}+13 n+4}\)

For Problems \(1-44\), solve each equation. $$ \frac{-3}{4 x+5}=\frac{2}{5 x-7} $$

Perform the indicated divisions. $$ \left(4 x^{3}-13 x^{2}+8 x-15\right) \div\left(4 x^{2}-x+5\right) $$

For Problems 41-64, simplify each complex fraction. $$ \frac{\frac{1}{2}-\frac{1}{4}}{\frac{5}{8}+\frac{3}{4}} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{3}{x}-\frac{5}{3 x^{2}}-\frac{7}{6 x} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{10 t^{3}+25 t}{20 t+10} \cdot \frac{2 t^{2}-t-1}{t^{5}-t}\)

For Problems 9-50, simplify each rational expression. \(\frac{4 x^{2} y+8 x y^{2}-12 y^{3}}{18 x^{3} y-12 x^{2} y^{2}-6 x y^{3}}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ \frac{y-b}{x}=m \text { for } y $$

For Problems \(1-44\), solve each equation. $$ \frac{7}{x+4}=\frac{3}{x-8} $$

Perform the indicated divisions. $$ \left(5 x^{3}+8 x^{2}-5 x-2\right) \div\left(5 x^{2}-2 x-1\right) $$

For Problems 41-64, simplify each complex fraction. $$ \frac{\frac{3}{8}+\frac{3}{4}}{\frac{5}{8}-\frac{7}{12}} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{7}{3 x^{2}}-\frac{9}{4 x}-\frac{5}{2 x} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{t^{4}-81}{t^{2}-6 t+9} \cdot \frac{6 t^{2}-11 t-21}{5 t^{2}+8 t-21}\)

For Problems 9-50, simplify each rational expression. \(\frac{3+x-2 x^{2}}{2+x-x^{2}}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ \frac{y-1}{x+6}=\frac{-2}{3} $$ for \(y\)

For Problems \(1-44\), solve each equation. $$ \frac{2 x}{x-2}+\frac{15}{x^{2}-7 x+10}=\frac{3}{x-5} $$

Perform the indicated divisions. $$ \left(5 a^{3}+7 a^{2}-2 a-9\right) \div\left(a^{2}+3 a-4\right) $$

For Problems 41-64, simplify each complex fraction. $$ \frac{\frac{3}{28}-\frac{5}{14}}{\frac{5}{7}+\frac{1}{4}} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{6}{5 t^{2}}-\frac{4}{7 t^{3}}+\frac{9}{5 t^{3}} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{4 t^{2}+t-5}{t^{3}-t^{2}} \cdot \frac{t^{4}+6 t^{3}}{16 t^{2}+40 t+25}\)

For Problems 9-50, simplify each rational expression. \(\frac{3 n^{2}+16 n-12}{7 n^{2}+44 n+12}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ \frac{y+5}{x-2}=\frac{3}{7} \text { for } y $$

Perform the indicated divisions. $$ \left(4 a^{3}-2 a^{2}+7 a-1\right) \div\left(a^{2}-2 a+3\right) $$

For Problems 41-64, simplify each complex fraction. $$ \frac{\frac{5}{9}+\frac{7}{36}}{\frac{3}{18}-\frac{5}{12}} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{5}{7 t}+\frac{3}{4 t^{2}}+\frac{1}{14 t} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{9 n^{2}-12 n+4}{n^{2}-4 n-32} \cdot \frac{n^{2}+4 n}{3 n^{3}-2 n^{2}}\)

For Problems 9-50, simplify each rational expression. \(\frac{x^{4}-2 x^{2}-15}{2 x^{4}+9 x^{2}+9}\)

Kent drives his Mazda 270 miles in the same time that it takes Dave to drive his Nissan 250 miles. If Kent averages 4 miles per hour faster than Dave, find their rates.

For Problems \(45-60\), set up an algebraic equation and solve each problem. A sum of \(\$ 1750\) is to be divided between two people in the ratio of 3 to 4 . How much does each person receive?

Perform the indicated divisions. $$ \left(2 n^{4}+3 n^{3}-2 n^{2}+3 n-4\right) \div\left(n^{2}+1\right) $$

For Problems 41-64, simplify each complex fraction. $$ \frac{\frac{5}{6 y}}{\frac{10}{3 x y}} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{5 b}{24 a^{2}}-\frac{11 a}{32 b} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{n r+3 n+2 r+6}{n r+3 n-3 r-9} \cdot \frac{n^{2}-9}{n^{3}-4 n}\)

For Problems 9-50, simplify each rational expression. \(\frac{8+18 x-5 x^{2}}{10+31 x+15 x^{2}}\)

Suppose that Wendy rides her bicycle 30 miles in the same time that it takes Kim to ride her bicycle 20 miles. If Wendy rides 5 miles per hour faster than Kim, find the rate of each.

Set up an algebraic equation and solve each problem. A blueprint has a scale where 1 inch represents 5 feet. Find the dimensions of a rectangular room that measures \(3 \frac{1}{2}\) inches by \(5 \frac{3}{4}\) inches on the blueprint.

Perform the indicated divisions. $$ \left(3 n^{4}+n^{3}-7 n^{2}-2 n+2\right) \div\left(n^{2}-2\right) $$

For Problems 41-64, simplify each complex fraction. $$ \frac{\frac{9}{8 x y^{2}}}{\frac{5}{4 x^{2}}} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{9}{14 x^{2} y}-\frac{4 x}{7 y^{2}} $$