Chapter 4

For Problems \(31-44\), solve each equation for the indicated variable. $$ y=\frac{3}{4} x-\frac{2}{3} \text { for } x $$

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

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

Perform the indicated operations, and express your answers in simplest form. $$ \frac{n-1}{n+4}+\frac{n}{n+6}+\frac{2 n+18}{n^{2}+10 n+24} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{5}{12 x}-\frac{9}{8 y} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{7 x y}{x^{2}-4 x+4} \div \frac{14 y}{x^{2}-4}\)

For Problems 9-50, simplify each rational expression. \(\frac{x^{2}-14 x+49}{6 x^{2}-37 x-35}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ \frac{-2}{x-4}=\frac{5}{y-1} \text { for } y $$

For Problems \(1-44\), solve each equation. $$ \frac{3 s}{s+2}+1=\frac{35}{2(3 s+1)} $$

Perform the indicated divisions. $$ \frac{4 a^{2}-8 a b+4 b^{2}}{a-b} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{4 x-3}{2 x^{2}+x-1}-\frac{2 x+7}{3 x^{2}+x-2}-\frac{3}{3 x-2} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{x^{2}-4 x y+4 y^{2}}{7 x y^{2}} \div \frac{4 x^{2}-3 x y-10 y^{2}}{20 x^{2} y+25 x y^{2}}\)

For Problems 9-50, simplify each rational expression. \(\frac{3 x^{2}+17 x-6}{9 x^{2}-6 x+1}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ \frac{7}{y-3}=\frac{3}{x+1} \text { for } y $$

For Problems \(1-44\), solve each equation. $$ \frac{s}{2 s-1}-3=\frac{-32}{3(s+5)} $$

Perform the indicated divisions. $$ \frac{3 x^{2}-2 x y-8 y^{2}}{x-2 y} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2 x+5}{x^{2}+3 x-18}-\frac{3 x-1}{x^{2}+4 x-12}+\frac{5}{x-2} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{7}{3 x}-\frac{8}{7 y}-2 $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{x^{2}+5 x y-6 y^{2}}{x y^{2}-y^{3}} \cdot \frac{2 x^{2}+15 x y+18 y^{2}}{x y+4 y^{2}}\)

For Problems 9-50, simplify each rational expression. \(\frac{9 y^{2}-1}{3 y^{2}+11 y-4}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ I=\frac{100 M}{C} \text { for } M $$

For Problems \(1-44\), solve each equation. $$ 2-\frac{3 x}{x-4}=\frac{14}{x+7} $$

Perform the indicated divisions. $$ \frac{4 x^{3}-5 x^{2}+2 x-6}{x^{2}-3 x} $$

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

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{7}{10 x^{2}}+\frac{11}{15 x} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{5-14 n-3 n^{2}}{1-2 n-3 n^{2}} \cdot \frac{9+7 n-2 n^{2}}{27-15 n+2 n^{2}}\)

For Problems 9-50, simplify each rational expression. \(\frac{2 x^{3}+3 x^{2}-14 x}{x^{2} y+7 x y-18 y}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ V=C\left(1-\frac{T}{N}\right) \text { for } T $$

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

Perform the indicated divisions. $$ \frac{3 x^{3}+2 x^{2}-5 x-1}{x^{2}+2 x} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2 n^{2}}{n^{4}-16}-\frac{n}{n^{2}-4}+\frac{1}{n+2} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{7}{12 a^{2}}-\frac{5}{16 a} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{6-n-2 n^{2}}{12-11 n+2 n^{2}} \cdot \frac{24-26 n+5 n^{2}}{2+3 n+n^{2}}\)

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

For Problems \(31-44\), solve each equation for the indicated variable. $$ \frac{R}{S}=\frac{T}{S+T} \quad \text { for } R $$

For Problems \(1-44\), solve each equation. $$ \frac{n+6}{27}=\frac{1}{n} $$

Perform the indicated divisions. $$ \frac{8 y^{3}-y^{2}-y+5}{y^{2}+y} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{15 x^{2}-10}{5 x^{2}-7 x+2}-\frac{3 x+4}{x-1}-\frac{2}{5 x-2} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{10}{7 n}-\frac{12}{4 n^{2}} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{3 x^{4}+2 x^{2}-1}{3 x^{4}+14 x^{2}-5} \cdot \frac{x^{4}-2 x^{2}-35}{x^{4}-17 x^{2}+70}\)

For Problems 9-50, simplify each rational expression. \(\frac{5 y^{2}+22 y+8}{25 y^{2}-4}\)

For Problems \(31-44\), solve each equation for the indicated variable. $$ \frac{1}{R}=\frac{1}{S}+\frac{1}{T} \text { for } R $$

For Problems \(1-44\), solve each equation. $$ \frac{n}{5}=\frac{10}{n-5} $$

Perform the indicated divisions. $$ \frac{5 y^{3}-6 y^{2}-7 y-2}{y^{2}-y} $$

Perform the indicated operations, and express your answers in simplest form. $$ \frac{2 n^{2}}{n^{4}-16}-\frac{n}{n^{2}-4}+\frac{1}{n+2} $$

Add or subtract the rational expressions as indicated. Be sure to express your answers in simplest form. $$ \frac{6}{8 n^{2}}-\frac{3}{5 n} $$

For Problems 13-50, perform the indicated operations involving rational expressions. Express final answers in simplest form. \(\frac{2 x^{4}+x^{2}-3}{2 x^{4}+5 x^{2}+2} \cdot \frac{3 x^{4}+10 x^{2}+8}{3 x^{4}+x^{2}-4}\)

For Problems 9-50, simplify each rational expression. \(\frac{16 x^{3} y+24 x^{2} y^{2}-16 x y^{3}}{24 x^{2} y+12 x y^{2}-12 y^{3}}\)

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

For Problems \(1-44\), solve each equation. $$ \frac{3 n}{n-1}-\frac{1}{3}=\frac{-40}{3 n-18} $$