Chapter 4

Perform the indicated operations, and express your answers in simplest form. $$ \frac{3 a}{8 a^{2}-2 a-3}+\frac{1}{4 a^{2}+13 a-12} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{3(y-2)}{7 y}+\frac{4(y-1)}{7 y} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{5 x y}{8 y^{2}} \cdot \frac{18 x^{2} y}{15}\)

For Problems 9-50, simplify each rational expression. \(\frac{-40 x^{3} y}{-24 x y^{4}}\)

For Problems \(1-44\), solve each equation. $$ n-\frac{3}{n}=\frac{26}{3} $$

Perform the indicated divisions. $$ \frac{12 x^{2}-32 x-35}{2 x-7} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2 a}{6 a^{2}+13 a-5}+\frac{a}{2 a^{2}+a-10} $$

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

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{4 x^{2}}{5 y^{2}} \cdot \frac{15 x y}{24 x^{2} y^{2}}\)

For Problems 9-50, simplify each rational expression. \(\frac{-30 x^{2} y^{2} z^{2}}{-35 x z^{3}}\)

Solve each equation. $$ \frac{-1}{2 x-5}+\frac{2 x-4}{4 x^{2}-25}=\frac{5}{6 x+15} $$

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

Perform the indicated divisions. $$ \frac{3 x^{3}+7 x^{2}-13 x-21}{x+3} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{5}{x^{2}+3}-\frac{2}{x^{2}+4 x-21} $$

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

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{5 x^{4}}{12 x^{2} y^{3}} \div \frac{9}{5 x y}\)

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

Solve each equation. $$ \frac{-2}{3 x+2}+\frac{x-1}{9 x^{2}-4}=\frac{3}{12 x-8} $$

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

Perform the indicated divisions. $$ \frac{4 x^{3}-21 x^{2}+3 x+10}{x-5} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{7}{x^{2}+1}-\frac{3}{x^{2}+7 x-60} $$

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

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{7 x^{2} y}{9 x y^{3}} \div \frac{3 x^{4}}{2 x^{2} y^{2}}\)

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

Solve each equation. $$ \frac{7 y+2}{12 y^{2}+11 y-15}-\frac{1}{3 y+5}=\frac{2}{4 y-3} $$

For Problems \(1-44\), solve each equation. $$ \frac{-2}{x-5}=\frac{1}{x+9} $$

Perform the indicated divisions. $$ \left(2 x^{3}+9 x^{2}-17 x+6\right) \div(2 x-1) $$

$$ \frac{3 x}{x^{2}-6 x+9}-\frac{2}{x-3} $$

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

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{9 a^{2} c}{12 b c^{2}} \div \frac{21 a b}{14 c^{3}}\)

For Problems 9-50, simplify each rational expression. \(\frac{18 x+12}{12 x-6}\)

Solve each equation. $$ \frac{5 y-4}{6 y^{2}+y-12}-\frac{2}{2 y+3}=\frac{5}{3 y-4} $$

For Problems \(1-44\), solve each equation. $$ \frac{5}{2 a-1}=\frac{-6}{3 a+2} $$

Perform the indicated divisions. $$ \left(3 x^{3}-5 x^{2}-23 x-7\right) \div(3 x+1) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{3}{x+4}+\frac{2 x}{x^{2}+8 x+16} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{a-4}{6}+\frac{4 a-1}{8} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{3 a b^{3}}{4 c} \div \frac{21 a c}{12 b c^{3}}\)

For Problems 9-50, simplify each rational expression. \(\frac{20 x+50}{15 x-30}\)

Solve each equation. $$ \frac{2 n}{6 n^{2}+7 n-3}-\frac{n-3}{3 n^{2}+11 n-4}=\frac{5}{2 n^{2}+11 n+12} $$

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

Perform the indicated divisions. $$ \left(4 x^{3}-x^{2}-2 x+6\right) \div(x-2) $$

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

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

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{9 x^{2} y^{3}}{14 x} \cdot \frac{21 y}{15 x y^{2}} \cdot \frac{10 x}{12 y^{3}}\)

For Problems 9-50, simplify each rational expression. \(\frac{a^{2}+7 a+10}{a^{2}-7 a-18}\)

Solve each equation. $$ \frac{x+1}{2 x^{2}+7 x-4}-\frac{x}{2 x^{2}-7 x+3}=\frac{1}{x^{2}+x-12} $$

For Problems \(1-44\), solve each equation. $$ \frac{x}{x-2}+1=\frac{8}{x-1} $$

Perform the indicated divisions. $$ \left(6 x^{3}-2 x^{2}+4 x-3\right) \div(x+1) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{6}{x^{2}-9}-\frac{9}{x^{2}-6 x+9} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{2 n+1}{9}-\frac{n+3}{12} $$