Solve {left(frac{1/2-frac{2/3right)}^2}{5/6}-sqrt{1/9}}{sqrt[3]{frac{1}{8}}+{left(1-frac{1}{2}right)}^2frac{9}{8}}

$$\frac{ \frac{ { \left( \frac{ 1 }{ 2 } - \frac{ 2 }{ 3 } \right) }^{ 2 } }{ \frac{ 5 }{ 6 } } - \sqrt{ \frac{ 1 }{ 9 } } }{ \sqrt[ 3 ]{ \frac{ 1 }{ 8 } } + { \left(1- \frac{ 1 }{ 2 } \right) }^{ 2 } \frac{ 9 }{ 8 } }$$

Evaluate

$$-\frac{48}{125}=-0.384$$

Solution Steps

Subtract \frac{2}{3} from \frac{1}{2} to get -\frac{1}{6}.

$$\frac{\frac{\left(-\frac{1}{6}\right)^{2}}{\frac{5}{6}}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calculate -\frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{\frac{\frac{1}{36}}{\frac{5}{6}}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Divide \frac{1}{36} by \frac{5}{6} by multiplying \frac{1}{36} by the reciprocal of \frac{5}{6}.

$$\frac{\frac{1}{36}\times \frac{6}{5}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Multiply \frac{1}{36} and \frac{6}{5} to get \frac{1}{30}.

$$\frac{\frac{1}{30}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Rewrite the square root of the division \frac{1}{9} as the division of square roots \frac{\sqrt{1}}{\sqrt{9}}. Take the square root of both numerator and denominator.

$$\frac{\frac{1}{30}-\frac{1}{3}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Subtract \frac{1}{3} from \frac{1}{30} to get -\frac{3}{10}.

$$\frac{-\frac{3}{10}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calculate \sqrt[3]{\frac{1}{8}} and get \frac{1}{2}.

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\left(\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\frac{1}{4}\times \frac{9}{8}}$$

Multiply \frac{1}{4} and \frac{9}{8} to get \frac{9}{32}.

$$\frac{-\frac{3}{10}}{\frac{1}{2}+\frac{9}{32}}$$

Add \frac{1}{2} and \frac{9}{32} to get \frac{25}{32}.

$$\frac{-\frac{3}{10}}{\frac{25}{32}}$$

Divide -\frac{3}{10} by \frac{25}{32} by multiplying -\frac{3}{10} by the reciprocal of \frac{25}{32}.

$$-\frac{3}{10}\times \frac{32}{25}$$

Multiply -\frac{3}{10} and \frac{32}{25} to get -\frac{48}{125}.

$$-\frac{48}{125}$$

Factor

$$-\frac{48}{125} = -0.384$$