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}}

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

Avaliar

$$-\frac{704}{1875}\approx -0,375466667$$

Passos Para a Resolução

Divida \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} por \frac{5}{6} ao multiplicar \frac{\left(\frac{1}{2}-\frac{2}{3}\right)^{2}}{\frac{5}{6}} pelo recíproco de \frac{5}{6}.

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

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

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

Calcule -\frac{1}{6} elevado a 2 e obtenha \frac{1}{36}.

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

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

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

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

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

Divida \frac{1}{6} por \frac{25}{6} ao multiplicar \frac{1}{6} pelo recíproco de \frac{25}{6}.

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

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

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

Reescreva a raiz quadrada da divisão \frac{1}{9} à medida que a divisão de raízes quadradas \frac{\sqrt{1}}{\sqrt{9}}. Calcule a raiz quadrada do numerador e do denominador.

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

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

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

Calcule \sqrt[3]{\frac{1}{8}} e obtenha \frac{1}{2}.

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

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

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

Calcule \frac{1}{2} elevado a 2 e obtenha \frac{1}{4}.

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

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

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

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

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

Divida -\frac{22}{75} por \frac{25}{32} ao multiplicar -\frac{22}{75} pelo recíproco de \frac{25}{32}.

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

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

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

Fatorizar

$$-\frac{704}{1875} = -0,37546666666666667$$