Chapter 4

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{5 x y}{7 a} \cdot \frac{14 a^{2}}{15 x} \cdot \frac{3 a}{8 y}\)

For Problems 9-50, simplify each rational expression. \(\frac{a^{2}+4 a-32}{3 a^{2}+26 a+16}\)

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

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

Perform the indicated divisions. $$ \left(x^{4}-10 x^{3}+19 x^{2}+33 x-18\right) \div(x-6) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2}{y^{2}+6 y-16}-\frac{4}{y+8}-\frac{3}{y-2} $$

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

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{3 x+6}{5 y} \cdot \frac{x^{2}+4}{x^{2}+10 x+16}\)

For Problems 9-50, simplify each rational expression. \(\frac{2 n^{2}+n-21}{10 n^{2}+33 n-7}\)

Solve each equation. $$ \frac{2}{n^{2}+4 n}+\frac{3}{n^{2}-3 n-28}=\frac{5}{n^{2}-6 n-7} $$

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

Perform the indicated divisions. $$ \left(x^{4}+2 x^{3}-16 x^{2}+x+6\right) \div(x-3) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{7}{y-6}-\frac{10}{y+12}+\frac{4}{y^{2}+6 y-72} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{4 x-3}{6}-\frac{8 x-2}{12} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{5 x y}{x+6} \cdot \frac{x^{2}-36}{x^{2}-6 x}\)

For Problems 9-50, simplify each rational expression. \(\frac{4 n^{2}-15 n-4}{7 n^{2}-30 n+8}\)

Solve each equation. $$ \frac{x+1}{x^{3}-9 x}-\frac{1}{2 x^{2}+x-21}=\frac{1}{2 x^{2}+13 x+21} $$

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

Perform the indicated divisions. $$ \frac{x^{3}-125}{x-5} $$

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

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{x-2}{5}-\frac{x+3}{6}+\frac{x+1}{15} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{5 a^{2}+20 a}{a^{3}-2 a^{2}} \cdot \frac{a^{2}-a-12}{a^{2}-16}\)

For Problems 9-50, simplify each rational expression. \(\frac{5 x^{2}+7}{10 x}\)

Solve each equation. $$ \frac{x}{2 x^{2}+5 x}-\frac{x}{2 x^{2}+7 x+5}=\frac{2}{x^{2}+x} $$

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

Perform the indicated divisions. $$ \frac{x^{3}+64}{x+4} $$

Perform the indicated operations, and express your answers in simplest form. $$ x+\frac{5}{x^{2}-25}-\frac{x^{2}}{x+5} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{x+1}{4}+\frac{x-3}{6}-\frac{x-2}{8} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{2 a^{2}+6}{a^{2}-a} \cdot \frac{a^{3}-a^{2}}{8 a-4}\)

For Problems 9-50, simplify each rational expression. \(\frac{12 x^{2}+11 x-15}{20 x^{2}-23 x+6}\)

Solve each equation. $$ \frac{4 t}{4 t^{2}-t-3}+\frac{2-3 t}{3 t^{2}-t-2}=\frac{1}{12 t^{2}+17 t+6} $$

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

Perform the indicated divisions. $$ \left(x^{3}+64\right) \div(x+1) $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{x+3}{x+10}+\frac{4 x-3}{x^{2}+8 x-20}+\frac{x-1}{x-2} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{3}{8 x}+\frac{7}{10 x} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{3 n^{2}+15 n-18}{3 n^{2}+10 n-48} \cdot \frac{6 n^{2}-n-40}{4 n^{2}+6 n-10}\)

For Problems 9-50, simplify each rational expression. \(\frac{6 x^{2}+x-15}{8 x^{2}-10 x-3}\)

Solve each equation. $$ \frac{2 t}{2 t^{2}+9 t+10}+\frac{1-3 t}{3 t^{2}+4 t-4}=\frac{4}{6 t^{2}+11 t-10} $$

For Problems \(1-44\), solve each equation. $$ \frac{x}{-4}=\frac{3}{12 x-25} $$

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

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2 x-1}{x+3}+\frac{x+4}{x-6}+\frac{3 x-1}{x^{2}-3 x-18} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{5}{6 x}-\frac{3}{10 x} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{6 n^{2}+11 n-10}{3 n^{2}+19 n-14} \cdot \frac{2 n^{2}+6 n-56}{2 n^{2}-3 n-20}\)

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

For Problems \(31-44\), solve each equation for the indicated variable. $$ y=\frac{5}{6} x+\frac{2}{9} \text { for } x $$

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

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

Perform the indicated operations, and express your answers in simplest form. $$ \frac{n}{n-6}+\frac{n+3}{n+8}+\frac{12 n+26}{n^{2}+2 n-48} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{9 y^{2}}{x^{2}+12 x+36} \div \frac{12 y}{x^{2}+6 x}\)

For Problems 9-50, simplify each rational expression. \(\frac{3 x^{2}-12 x}{x^{3}-64}\)