Chapter 2

In \(3-12,\) multiply and express each product in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{b+1}{4} \cdot \frac{12}{5 b+5} $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{\frac{1}{6}+\frac{1}{4}}{\frac{1}{3}+\frac{1}{2}}\)

Write each ratio in simplest form. \(6 a : 9 a, a \neq 0\)

List the values of the variables for which the rational expression is undefined. \(\frac{2 a}{2 a-7}\)

In \(3-7,\) write the reciprocal (multiplicative inverse) of each given number. $$ 1 $$

In \(3-14,\) solve and check each inequality. $$ \frac{7}{2 x}-\frac{2}{x}>\frac{3}{2} $$

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. $$ \frac{a+5}{5 a}-\frac{a-8}{8 a} $$

In \(3-20,\) solve each equation and check. $$ x-0.05 x=19 $$

In \(3-12,\) multiply and express each product in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{a^{2}-100}{3 a} \cdot \frac{a^{2}}{2 a-20} $$

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

Write each ratio in simplest form. \(\frac{18}{27}\)

List the values of the variables for which the rational expression is undefined. \(\frac{b+3}{b^{2}+b-6}\)

In \(8-12,\) write each rational number as a repeating decimal. $$ \frac{1}{6} $$

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. $$ \frac{2 x+3}{6 x}-\frac{x-2}{4 x} $$

In \(3-20,\) solve each equation and check. $$ 0.4 x+8=0.5 x $$

In \(3-12,\) multiply and express each product in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{7 y+21}{7 y} \cdot \frac{3}{y^{2}-9} $$

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

Write each ratio in simplest form. \(\frac{24}{72}\)

List the values of the variables for which the rational expression is undefined. \(\frac{4 c}{2 c^{2}-2 c}\)

In \(8-12,\) write each rational number as a repeating decimal. $$ \frac{2}{9} $$

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. $$ \frac{a+1}{3 a}+\frac{3}{2} $$

In \(3-20,\) solve each equation and check. $$ 0.2 a=0.05 a+3 $$

In \(3-12,\) multiply and express each product in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{a^{2}-5 a+4}{3 a+6} \cdot \frac{2 a+4}{a^{2}-16} $$

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

Write each ratio in simplest form. \(\frac{10 x}{35 x}, x \neq 0\)

List the values of the variables for which the rational expression is undefined. \(\frac{5}{x^{3}-5 x^{2}-6 x}\)

In \(8-12,\) write each rational number as a repeating decimal. $$ \frac{5}{7} $$

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. $$ 3+\frac{2}{x} $$

In \(3-20,\) solve each equation and check. $$ 1.2 b-3=7-0.05 b $$

In \(3-12,\) multiply and express each product in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{2 a+4}{6 a} \cdot \frac{3 a^{2}}{a^{2}+2 a} $$

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

Solve each proportion for the variable. \(\frac{x}{8}=\frac{6}{24}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{6}{10}\)

In \(8-12,\) write each rational number as a repeating decimal. $$ \frac{2}{15} $$

In \(3-14,\) solve and check each inequality. $$ \frac{2}{x}+\frac{3}{x}<10 $$

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. $$ 5-\frac{1}{2 y} $$

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

In \(3-12,\) multiply and express each product in simplest form. In each case, list any values of the variables for which the fractions are not defined. $$ \frac{6-2 x}{x^{2}-9} \cdot \frac{15+5 x}{4 x} $$

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

Solve each proportion for the variable. \(\frac{x-1}{15}=\frac{2}{5}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{5 a^{2} b}{10 a}\)

In \(8-12,\) write each rational number as a repeating decimal. $$ \frac{7}{8} $$

In \(3-14,\) solve and check each inequality. $$ \frac{x}{x+5}-\frac{1}{x+5}>4 $$

Simplify each complex rational expression. In each case, list any values of the variables for which the fractions are not defined. \(\frac{4 y-\frac{1}{y}}{y-\frac{1}{2}}\)

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. $$ a-\frac{3}{2 a} $$

In \(3-20,\) solve each equation and check. $$ \frac{7}{2 x-3}=\frac{4}{x} $$

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. $$ \frac{3}{4} \div \frac{9}{20} $$

Solve each proportion for the variable. \(\frac{a-2}{2 a}=\frac{5}{14}\)

Write each rational expression in simplest form and list the values of the variables for which the fraction is undefined. \(\frac{12 x y^{2}}{3 x^{2} y}\)

In \(13-22,\) write each decimal as a common fraction. $$ 0.125 $$