Solucionar {[5/4-(-2+3/4)^2]:(5/4)^2-(-2)^3}:[43/5-(-frac{4}{5})^2*(2-frac{3}{4})]

$$\{ [ \frac { 5 } { 4 } - ( - 2 + \frac { 3 } { 4 } ) ^ { 2 } ] : ( \frac { 5 } { 4 } ) ^ { 2 } - ( - 2 ) ^ { 3 } \} : [ \frac { 43 } { 5 } - ( - \frac { 4 } { 5 } ) ^ { 2 } \cdot ( 2 - \frac { 3 } { 4 } ) ]$$

Calcular

$$1$$

Pasos de la solución

Suma -2 y \frac{3}{4} para obtener -\frac{5}{4}.

$$\frac{\frac{\frac{5}{4}-\left(-\frac{5}{4}\right)^{2}}{\left(\frac{5}{4}\right)^{2}}-\left(-2\right)^{3}}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Calcula -\frac{5}{4} a la potencia de 2 y obtiene \frac{25}{16}.

$$\frac{\frac{\frac{5}{4}-\frac{25}{16}}{\left(\frac{5}{4}\right)^{2}}-\left(-2\right)^{3}}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Resta \frac{25}{16} de \frac{5}{4} para obtener -\frac{5}{16}.

$$\frac{\frac{-\frac{5}{16}}{\left(\frac{5}{4}\right)^{2}}-\left(-2\right)^{3}}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Calcula \frac{5}{4} a la potencia de 2 y obtiene \frac{25}{16}.

$$\frac{\frac{-\frac{5}{16}}{\frac{25}{16}}-\left(-2\right)^{3}}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Divide -\frac{5}{16} por \frac{25}{16} al multiplicar -\frac{5}{16} por el recíproco de \frac{25}{16}.

$$\frac{-\frac{5}{16}\times \frac{16}{25}-\left(-2\right)^{3}}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Multiplica -\frac{5}{16} y \frac{16}{25} para obtener -\frac{1}{5}.

$$\frac{-\frac{1}{5}-\left(-2\right)^{3}}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Calcula -2 a la potencia de 3 y obtiene -8.

$$\frac{-\frac{1}{5}-\left(-8\right)}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

El opuesto de -8 es 8.

$$\frac{-\frac{1}{5}+8}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Suma -\frac{1}{5} y 8 para obtener \frac{39}{5}.

$$\frac{\frac{39}{5}}{\frac{43}{5}-\left(-\frac{4}{5}\right)^{2}\left(2-\frac{3}{4}\right)}$$

Calcula -\frac{4}{5} a la potencia de 2 y obtiene \frac{16}{25}.

$$\frac{\frac{39}{5}}{\frac{43}{5}-\frac{16}{25}\left(2-\frac{3}{4}\right)}$$

Resta \frac{3}{4} de 2 para obtener \frac{5}{4}.

$$\frac{\frac{39}{5}}{\frac{43}{5}-\frac{16}{25}\times \frac{5}{4}}$$

Multiplica \frac{16}{25} y \frac{5}{4} para obtener \frac{4}{5}.

$$\frac{\frac{39}{5}}{\frac{43}{5}-\frac{4}{5}}$$

Resta \frac{4}{5} de \frac{43}{5} para obtener \frac{39}{5}.

$$\frac{\frac{39}{5}}{\frac{39}{5}}$$

Divide \frac{39}{5} entre \frac{39}{5} para obtener 1.

$$1$$

Factorizar

$$1$$