Resolver {left(frac{1/2-frac{2/3right)}^2}{5/6}div5/6-sqrt{frac{1}{9}}}{sqrt[3]{frac{1}{8}}+{left(1-frac{1}{2}right)}^2frac{9}{8}}

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

Calcular

$$-\frac{704}{1875}\approx -0.375466667$$

Pasos da solución

Divide \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} entre \frac{5}{6} mediante a multiplicación de \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} polo recíproco de \frac{5}{6}.

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

Resta \frac{2}{3} de \frac{1}{2} para obter -\frac{1}{6}.

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

Calcula -\frac{1}{6} á potencia de 2 e obtén \frac{1}{36}.

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

Multiplica \frac{1}{36} e 6 para obter \frac{1}{6}.

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

Multiplica \frac{5}{6} e 5 para obter \frac{25}{6}.

$$\frac{\frac{\frac{1}{6}}{\frac{25}{6}}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Divide \frac{1}{6} entre \frac{25}{6} mediante a multiplicación de \frac{1}{6} polo recíproco de \frac{25}{6}.

$$\frac{\frac{1}{6}\times \frac{6}{25}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Multiplica \frac{1}{6} e \frac{6}{25} para obter \frac{1}{25}.

$$\frac{\frac{1}{25}-\sqrt{\frac{1}{9}}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Reescribe a raíz cadrada da división \frac{1}{9} como a división de raíces cadradas \frac{\sqrt{1}}{\sqrt{9}}. Obtén a raíz cadrada do numerador e o denominador.

$$\frac{\frac{1}{25}-\frac{1}{3}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Resta \frac{1}{3} de \frac{1}{25} para obter -\frac{22}{75}.

$$\frac{-\frac{22}{75}}{\sqrt[3]{\frac{1}{8}}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calcular \sqrt[3]{\frac{1}{8}} e obter \frac{1}{2}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\left(1-\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Resta \frac{1}{2} de 1 para obter \frac{1}{2}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\left(\frac{1}{2}\right)^{2}\times \frac{9}{8}}$$

Calcula \frac{1}{2} á potencia de 2 e obtén \frac{1}{4}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\frac{1}{4}\times \frac{9}{8}}$$

Multiplica \frac{1}{4} e \frac{9}{8} para obter \frac{9}{32}.

$$\frac{-\frac{22}{75}}{\frac{1}{2}+\frac{9}{32}}$$

Suma \frac{1}{2} e \frac{9}{32} para obter \frac{25}{32}.

$$\frac{-\frac{22}{75}}{\frac{25}{32}}$$

Divide -\frac{22}{75} entre \frac{25}{32} mediante a multiplicación de -\frac{22}{75} polo recíproco de \frac{25}{32}.

$$-\frac{22}{75}\times \frac{32}{25}$$

Multiplica -\frac{22}{75} e \frac{32}{25} para obter -\frac{704}{1875}.

$$-\frac{704}{1875}$$

Factorizar

$$-\frac{704}{1875} = -0.37546666666666667$$