Resolver [-1+3/2-(-3/4-(-1-1/6))]sqrt{2-frac{7/4}}{(-frac{5}{3})^-1+frac{1}{2}-(-2)^-2}

$$\frac { [ - 1 + \frac { 3 } { 2 } - ( - \frac { 3 } { 4 } - ( - 1 - \frac { 1 } { 6 } ) ) ] \sqrt { 2 - \frac { 7 } { 4 } } } { ( - \frac { 5 } { 3 } ) ^ { - 1 } + \frac { 1 } { 2 } - ( - 2 ) ^ { - 2 } }$$

Avaliar

$$-\frac{5}{42}\approx -0,119047619$$

Passos Para a Resolução

Some -1 e \frac{3}{2} para obter \frac{1}{2}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}-\left(-1-\frac{1}{6}\right)\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Subtraia \frac{1}{6} de -1 para obter -\frac{7}{6}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}-\left(-\frac{7}{6}\right)\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

O oposto de -\frac{7}{6} é \frac{7}{6}.

$$\frac{\left(\frac{1}{2}-\left(-\frac{3}{4}+\frac{7}{6}\right)\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Some -\frac{3}{4} e \frac{7}{6} para obter \frac{5}{12}.

$$\frac{\left(\frac{1}{2}-\frac{5}{12}\right)\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Subtraia \frac{5}{12} de \frac{1}{2} para obter \frac{1}{12}.

$$\frac{\frac{1}{12}\sqrt{2-\frac{7}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Subtraia \frac{7}{4} de 2 para obter \frac{1}{4}.

$$\frac{\frac{1}{12}\sqrt{\frac{1}{4}}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Reescreva a raiz quadrada da divisão \frac{1}{4} à medida que a divisão de raízes quadradas \frac{\sqrt{1}}{\sqrt{4}}. Calcule a raiz quadrada do numerador e do denominador.

$$\frac{\frac{1}{12}\times \frac{1}{2}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Multiplique \frac{1}{12} e \frac{1}{2} para obter \frac{1}{24}.

$$\frac{\frac{1}{24}}{\left(-\frac{5}{3}\right)^{-1}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Calcule -\frac{5}{3} elevado a -1 e obtenha -\frac{3}{5}.

$$\frac{\frac{1}{24}}{-\frac{3}{5}+\frac{1}{2}-\left(-2\right)^{-2}}$$

Some -\frac{3}{5} e \frac{1}{2} para obter -\frac{1}{10}.

$$\frac{\frac{1}{24}}{-\frac{1}{10}-\left(-2\right)^{-2}}$$

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

$$\frac{\frac{1}{24}}{-\frac{1}{10}-\frac{1}{4}}$$

Subtraia \frac{1}{4} de -\frac{1}{10} para obter -\frac{7}{20}.

$$\frac{\frac{1}{24}}{-\frac{7}{20}}$$

Divida \frac{1}{24} por -\frac{7}{20} ao multiplicar \frac{1}{24} pelo recíproco de -\frac{7}{20}.

$$\frac{1}{24}\left(-\frac{20}{7}\right)$$

Multiplique \frac{1}{24} e -\frac{20}{7} para obter -\frac{5}{42}.

$$-\frac{5}{42}$$

Fatorizar

$$-\frac{5}{42} = -0,11904761904761904$$