Solve {(2/7)^-1-(frac{3/5)^-1}}{(3/2)^-2}

$$\frac { \{ ( \frac { 2 } { 7 } ) ^ { - 1 } - ( \frac { 3 } { 5 } ) ^ { - 1 } \} } { ( \frac { 3 } { 2 } ) ^ { - 2 } }$$

Evaluate

$$\frac{33}{8}=4.125$$

Solution Steps

Calculate \frac{2}{7} to the power of -1 and get \frac{7}{2}.

$$\frac{\frac{7}{2}-\left(\frac{3}{5}\right)^{-1}}{\left(\frac{3}{2}\right)^{-2}}$$

Calculate \frac{3}{5} to the power of -1 and get \frac{5}{3}.

$$\frac{\frac{7}{2}-\frac{5}{3}}{\left(\frac{3}{2}\right)^{-2}}$$

Subtract \frac{5}{3} from \frac{7}{2} to get \frac{11}{6}.

$$\frac{\frac{11}{6}}{\left(\frac{3}{2}\right)^{-2}}$$

Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$\frac{\frac{11}{6}}{\frac{4}{9}}$$

Divide \frac{11}{6} by \frac{4}{9} by multiplying \frac{11}{6} by the reciprocal of \frac{4}{9}.

$$\frac{11}{6}\times \frac{9}{4}$$

Multiply \frac{11}{6} and \frac{9}{4} to get \frac{33}{8}.

$$\frac{33}{8}$$

Factor

$$\frac{3 \cdot 11}{2 ^ {3}} = 4\frac{1}{8} = 4.125$$