Chapter 2

In \(3-14,\) solve and check each inequality. $$ 3-\frac{9}{a+1}>5-\frac{1}{a+1} $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{\frac{1}{2 x}+\frac{1}{3 x}}{\frac{1}{x^{2}}}\)

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{1}{x}+1 $$

In \(3-20,\) solve each equation and check. $$ \frac{3}{a}+\frac{1}{2}=\frac{11}{5 a} $$

In \(13-24,\) divide and express each quotient in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{12}{a} \div \frac{6}{4 a} $$

Solve each proportion for the variable. \(\frac{y+3}{y+8}=\frac{6}{15}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{14 b^{4}}{21 b^{3}}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0 . \overline{6} $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{a-\frac{49}{a}}{a-9+\frac{14}{a}}\)

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{3}{x+2}+\frac{x-2}{x} $$

In \(3-20,\) solve each equation and check. $$ 18-\frac{4}{b}=10 $$

Solve each proportion for the variable. \(\frac{3 x+3}{16}=\frac{2 x+1}{10}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{9 c d^{2}}{12 c^{4} d^{2}}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0 . \overline{2} $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{3-\frac{9}{x}}{x-8+\frac{15}{x}}\)

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{b}{b-1}-\frac{1}{2-2 b} $$

In \(3-20,\) solve each equation and check. $$ \frac{x}{2}=\frac{3}{2 x+1} $$

In \(13-24,\) divide and express each quotient in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{a^{2}}{8 a} \div \frac{3 a}{4} $$

Solve each proportion for the variable. \(\frac{2}{x-1}=\frac{x+2}{2}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{8 a+16}{12 a}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0 . \overline{36} $$

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{1}{2-x}+\frac{2}{x-2} $$

In \(3-20,\) solve each equation and check. $$ 1=\frac{5}{x+3}+\frac{5}{(x+2)(x+3)} $$

In \(13-24,\) divide and express each quotient in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{x-2}{3 x} \div \frac{4 x-8}{9} $$

Solve each proportion for the variable. \(\frac{4 x-8}{3}=\frac{8}{x-3}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{9 y^{2}+3 y}{6 y^{2}}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0 . \overline{108} $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{1+\frac{1}{y}-\frac{6}{y^{2}}}{1+\frac{11}{y}+\frac{24}{y^{2}}}\)

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{1}{a^{2}-a-6}-\frac{1}{2 a^{2}-7 a+3} $$

In \(3-20,\) solve each equation and check. $$ \frac{a-1}{4}=\frac{8}{a+3} $$

In \(13-24,\) divide and express each quotient in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{6 y^{2}-3 y}{3 y} \div \frac{4 y^{2}-1}{2} $$

Solve each proportion for the variable. \(\frac{x-2}{x}=\frac{3}{x+2}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{8 a b-4 b^{2}}{6 a b}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0.15 \overline{6} $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{\frac{1}{a}-1}{1-\frac{1}{a}}\)

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{2}{a^{2}-4}-\frac{1}{a^{2}+2 a} $$

In \(3-20,\) solve each equation and check. $$ \frac{4}{y+2}=1-\frac{8}{y(y+2)} $$

In \(13-24,\) divide and express each quotient in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{c^{2}-6 c+9}{5 c-15} \div \frac{c-3}{5} $$

Solve each proportion for the variable. \(\frac{x}{5}=\frac{x+4}{x+13}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{10 d}{15 d-20 d^{2}}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0.8 \overline{3} $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{5-\frac{45}{a^{2}}}{\frac{3}{a}-1}\)

In \(3-20\) , perform the indicated additions or subtractions and write the result in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{1}{x}+\frac{1}{x-2}-\frac{2}{x^{2}-2 x} $$

In \(3-20,\) solve each equation and check. $$ \frac{4}{3 b-2}-\frac{7}{3 b+2}=\frac{1}{9 b^{2}-4} $$

In \(13-24,\) divide and express each quotient in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{w^{2}-w}{5 w} \div \frac{w^{2}-1}{5} $$

The ratio of the length to the width of a rectangle is 5 : 4. The perimeter of the rectangle is 72 inches. What are the dimensions of the rectangle?

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{8 c^{2}}{8 c^{2}+16 c}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0.5 \overline{7} $$

Simplify each expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{3}{2 x}-\frac{1+\frac{1}{x}}{x+1}\)

In \(21-24,\) the length and width of a rectangle are expressed in terms of a variable. a. Express each perimeter in terms of the variable. b. Express each area in terms of the variable. $$ l=2 x \text { and } w=\frac{1}{x} $$