Chapter 4

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{1}{5}+\frac{5}{6}-\frac{7}{15}\)

For Problems 9-50, simplify each rational expression. \(\frac{12 x y}{42 y}\)

Solve each equation. $$ 3+\frac{9}{n-3}=\frac{27}{n^{2}-3 n} $$

For Problems \(1-44\), solve each equation. $$ \frac{5}{7 x}-\frac{5}{6}=\frac{1}{6 x} $$

Perform the indicated divisions of polynomials by monomials. $$ \frac{-27 a^{3} b^{4}-36 a^{2} b^{3}+72 a^{2} b^{5}}{9 a^{2} b^{2}} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{3 n}{n^{2}-36}-\frac{2}{5 n+30} $$

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{2}{3}-\frac{7}{8}+\frac{1}{4}\)

For Problems 9-50, simplify each rational expression. \(\frac{21 x y}{35 x}\)

Solve each equation. $$ \frac{2}{n-2}-\frac{n}{n+5}=\frac{10 n+15}{n^{2}+3 n-10} $$

For Problems \(1-44\), solve each equation. $$ \frac{47-n}{n}=8+\frac{2}{n} $$

For Problems 11-52, perform the indicated divisions. $$ \frac{x^{2}-7 x-78}{x+6} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{5}{x}-\frac{5 x-30}{x^{2}+6 x}+\frac{x}{x+6} $$

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{1}{3}-\frac{1}{4}-\frac{3}{14}\)

For Problems 9-50, simplify each rational expression. \(\frac{18 a^{2}}{45 a b}\)

Solve each equation. $$ \frac{n}{n+3}+\frac{1}{n-4}=\frac{11-n}{n^{2}-n-12} $$

For Problems \(1-44\), solve each equation. $$ \frac{45-n}{n}=6+\frac{3}{n} $$

Perform the indicated divisions. $$ \frac{x^{2}+11 x-60}{x-4} $$

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

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{5}{6}-\frac{7}{9}-\frac{3}{10}\)

For Problems 9-50, simplify each rational expression. \(\frac{48 a b}{84 b^{2}}\)

Solve each equation. $$ \frac{2}{2 x-3}-\frac{2}{10 x^{2}-13 x-3}=\frac{x}{5 x+1} $$

For Problems \(1-44\), solve each equation. $$ \frac{n}{65-n}=8+\frac{2}{65-n} $$

Perform the indicated divisions. $$ \left(x^{2}+12 x-160\right) \div(x-8) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{3}{x^{2}+9 x+14}+\frac{5}{2 x^{2}+15 x+7} $$

For Problems \(13-66\), add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{2 x}{x-1}+\frac{4}{x-1} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{6 x y}{9 y^{4}} \cdot \frac{30 x^{3} y}{-48 x}\)

For Problems 9-50, simplify each rational expression. \(\frac{-14 y^{3}}{56 x y^{2}}\)

Solve each equation. $$ \frac{1}{3 x+4}+\frac{6}{6 x^{2}+5 x-4}=\frac{x}{2 x-1} $$

For Problems \(1-44\), solve each equation. $$ \frac{n}{70-n}=7+\frac{6}{70-n} $$

Perform the indicated divisions. $$ \left(x^{2}-18 x-175\right) \div(x+7) $$

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

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{-14 x y^{4}}{18 y^{2}} \cdot \frac{24 x^{2} y^{3}}{35 y^{2}}\)

For Problems 9-50, simplify each rational expression. \(\frac{-14 x^{2} y^{3}}{63 x y^{2}}\)

Solve each equation. $$ \frac{2 x}{x+3}-\frac{3}{x-6}=\frac{29}{x^{2}-3 x-18} $$

For Problems \(1-44\), solve each equation. $$ n+\frac{1}{n}=\frac{17}{4} $$

Perform the indicated divisions. $$ \frac{2 x^{2}-x-4}{x-1} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{1}{a^{2}-3 a-10}-\frac{4}{a^{2}+4 a-45} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{4 a}{a+2}+\frac{8}{a+2} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{5 a^{2} b^{2}}{11 a b} \cdot \frac{22 a^{3}}{15 a b^{2}}\)

For Problems 9-50, simplify each rational expression. \(\frac{54 c^{2} d}{-78 c d^{2}}\)

Solve each equation. $$ \frac{x}{x-4}-\frac{2}{x+8}=\frac{63}{x^{2}+4 x-32} $$

For Problems \(1-44\), solve each equation. $$ n+\frac{1}{n}=\frac{37}{6} $$

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

Perform the indicated operations, and express your answers in simplest form. $$ \frac{6}{a^{2}-3 a-54}-\frac{10}{a^{2}+5 a-6} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{6 a}{a-3}-\frac{18}{a-3} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{10 a^{2}}{5 b^{2}} \cdot \frac{15 b^{3}}{2 a^{4}}\)

For Problems 9-50, simplify each rational expression. \(\frac{60 x^{3} z}{-64 x y z^{2}}\)

Solve each equation. $$ \frac{a}{a-5}+\frac{2}{a-6}=\frac{2}{a^{2}-11 a+30} $$

For Problems \(1-44\), solve each equation. $$ n-\frac{2}{n}=\frac{23}{5} $$

Perform the indicated divisions. $$ \frac{15 x^{2}+22 x-5}{3 x+5} $$