Chapter 4

For Problems 1-30, solve each equation. $$ \frac{x}{4 x-4}+\frac{5}{x^{2}-1}=\frac{1}{4} $$

For Problems \(1-44\), solve each equation. $$ \frac{x+1}{4}+\frac{x-2}{6}=\frac{3}{4} $$

For Problems \(1-10\), perform the indicated divisions of polynomials by monomials. $$ \frac{9 x^{4}+18 x^{3}}{3 x} $$

For Problems 1 - 40, perform the indicated operations, and express your answers in simplest form. $$ \frac{2 x}{x^{2}+4 x}+\frac{5}{x} $$

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{1}{4}+\frac{5}{6}\)

For Problems 1-8, express each rational number in reduced form. \(\frac{27}{36}\)

For Problems 1-30, solve each equation. $$ \frac{x}{3 x-6}+\frac{4}{x^{2}-4}=\frac{1}{3} $$

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

Perform the indicated divisions of polynomials by monomials. $$ \frac{12 x^{3}-24 x^{2}}{6 x^{2}} $$

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

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

For Problems 1-8, express each rational number in reduced form. \(\frac{14}{21}\)

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

Perform the indicated divisions of polynomials by monomials. $$ \frac{-24 x^{6}+36 x^{8}}{4 x^{2}} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{4}{x^{2}+7 x}-\frac{1}{x} $$

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{7}{8}-\frac{3}{5}\)

For Problems 1-8, express each rational number in reduced form. \(\frac{45}{54}\)

For Problems \(1-44\), solve each equation. $$ \frac{x+4}{3}-\frac{x-5}{9}=1 $$

Perform the indicated divisions of polynomials by monomials. $$ \frac{-35 x^{5}-42 x^{3}}{-7 x^{2}} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{-10}{x^{2}-9 x}-\frac{2}{x} $$

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

For Problems 1-8, express each rational number in reduced form. \(\frac{-14}{42}\)

For Problems 1-30, solve each equation. $$ \frac{3}{n-5}+\frac{4}{n+7}=\frac{2 n+11}{n^{2}+2 n-35} $$

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

Perform the indicated divisions of polynomials by monomials. $$ \frac{15 a^{3}-25 a^{2}-40 a}{5 a} $$

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

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{6}{5}+\frac{1}{-4}\)

For Problems 1-8, express each rational number in reduced form. \(\frac{24}{-60}\)

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

For Problems \(1-44\), solve each equation. $$ \frac{3}{n}+\frac{1}{6}=\frac{11}{3 n} $$

Perform the indicated divisions of polynomials by monomials. $$ \frac{-16 a^{4}+32 a^{3}-56 a^{2}}{-8 a} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2 x}{x^{2}-16}+\frac{7}{x-4} $$

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{7}{8}+\frac{5}{-12}\)

For Problems 1-8, express each rational number in reduced form. \(\frac{45}{-75}\)

Solve each equation. $$ \frac{5 x}{2 x+6}-\frac{4}{x^{2}-9}=\frac{5}{2} $$

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

Perform the indicated divisions of polynomials by monomials. $$ \frac{13 x^{3}-17 x^{2}+28 x}{-x} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{6 a+4}{a^{2}-1}-\frac{5}{a-1} $$

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{8}{15}+\frac{3}{25}\)

For Problems 1-8, express each rational number in reduced form. \(\frac{-16}{-56}\)

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

For Problems \(1-44\), solve each equation. $$ \frac{9}{4 x}+\frac{1}{3}=\frac{5}{2 x} $$

Perform the indicated divisions of polynomials by monomials. $$ \frac{14 x y-16 x^{2} y^{2}-20 x^{3} y^{4}}{-x y} $$

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

For Problems 1-12, perform the indicated operations involving rational numbers. Be sure to express your answers in reduced form. \(\frac{5}{9}-\frac{11}{12}\)

For Problems 1-8, express each rational number in reduced form. \(\frac{-30}{-42}\)

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

For Problems \(1-44\), solve each equation. $$ \frac{3}{4 x}+\frac{5}{6}=\frac{4}{3 x} $$

Perform the indicated divisions of polynomials by monomials. $$ \frac{-18 x^{2} y^{2}+24 x^{3} y^{2}-48 x^{2} y^{3}}{6 x y} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2 n}{n^{2}-25}-\frac{3}{4 n+20} $$