Resolver sqrt{(40+1/2)(2-1)}-(2/3-1)^-2:(1/5)^-1/(1-frac{1{4})^2}+frac{(frac{2-frac{1}{3}}{frac{3}{2}-1})^-2}{frac{frac{1}{2}-frac{2}{3}}{4-frac{2}{3}}}

$$\sqrt { ( 40 + \frac { 1 } { 2 } ) ( 2 - 1 ) } - \frac { ( \frac { 2 } { 3 } - 1 ) ^ { - 2 } : ( \frac { 1 } { 5 } ) ^ { - 1 } } { ( 1 - \frac { 1 } { 4 } ) ^ { 2 } } + \frac { ( \frac { 2 - \frac { 1 } { 3 } } { \frac { 3 } { 2 } - 1 } ) ^ { - 2 } } { \frac { \frac { 1 } { 2 } - \frac { 2 } { 3 } } { 4 - \frac { 2 } { 3 } } }$$

Calcular

$$\frac{9\sqrt{2}}{2}-5\approx 1.363961031$$

Pasos de solución curta

Suma 40 e \frac{1}{2} para obter \frac{81}{2}.

$$\sqrt{\frac{81}{2}\left(2-1\right)}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Resta 1 de 2 para obter 1.

$$\sqrt{\frac{81}{2}\times 1}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Multiplica \frac{81}{2} e 1 para obter \frac{81}{2}.

$$\sqrt{\frac{81}{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Reescribe a raíz cadrada da división \sqrt{\frac{81}{2}} como a división de raíces cadradas \frac{\sqrt{81}}{\sqrt{2}}.

$$\frac{\sqrt{81}}{\sqrt{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Calcular a raíz cadrada de 81 e obter 9.

$$\frac{9}{\sqrt{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Racionaliza o denominador de \frac{9}{\sqrt{2}} mediante a multiplicación do numerador e o denominador por \sqrt{2}.

$$\frac{9\sqrt{2}}{\left(\sqrt{2}\right)^{2}}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

O cadrado de \sqrt{2} é 2.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{\left(\frac{2}{3}-1\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

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

$$\frac{9\sqrt{2}}{2}-\frac{\frac{\left(-\frac{1}{3}\right)^{-2}}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Calcula -\frac{1}{3} á potencia de -2 e obtén 9.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{\left(\frac{1}{5}\right)^{-1}}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Calcula \frac{1}{5} á potencia de -1 e obtén 5.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{5}}{\left(1-\frac{1}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Resta \frac{1}{4} de 1 para obter \frac{3}{4}.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{5}}{\left(\frac{3}{4}\right)^{2}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Calcula \frac{3}{4} á potencia de 2 e obtén \frac{9}{16}.

$$\frac{9\sqrt{2}}{2}-\frac{\frac{9}{5}}{\frac{9}{16}}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Divide \frac{9}{5} entre \frac{9}{16} mediante a multiplicación de \frac{9}{5} polo recíproco de \frac{9}{16}.

$$\frac{9\sqrt{2}}{2}-\frac{9}{5}\times \frac{16}{9}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Multiplica \frac{9}{5} e \frac{16}{9} para obter \frac{16}{5}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{2-\frac{1}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Resta \frac{1}{3} de 2 para obter \frac{5}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{\frac{5}{3}}{\frac{3}{2}-1}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

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

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{\frac{5}{3}}{\frac{1}{2}}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Divide \frac{5}{3} entre \frac{1}{2} mediante a multiplicación de \frac{5}{3} polo recíproco de \frac{1}{2}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{5}{3}\times 2\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Multiplica \frac{5}{3} e 2 para obter \frac{10}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\left(\frac{10}{3}\right)^{-2}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

Calcula \frac{10}{3} á potencia de -2 e obtén \frac{9}{100}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{\frac{\frac{1}{2}-\frac{2}{3}}{4-\frac{2}{3}}}$$

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

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{\frac{-\frac{1}{6}}{4-\frac{2}{3}}}$$

Resta \frac{2}{3} de 4 para obter \frac{10}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{\frac{-\frac{1}{6}}{\frac{10}{3}}}$$

Divide -\frac{1}{6} entre \frac{10}{3} mediante a multiplicación de -\frac{1}{6} polo recíproco de \frac{10}{3}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{-\frac{1}{6}\times \frac{3}{10}}$$

Multiplica -\frac{1}{6} e \frac{3}{10} para obter -\frac{1}{20}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{\frac{9}{100}}{-\frac{1}{20}}$$

Divide \frac{9}{100} entre -\frac{1}{20} mediante a multiplicación de \frac{9}{100} polo recíproco de -\frac{1}{20}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}+\frac{9}{100}\left(-20\right)$$

Multiplica \frac{9}{100} e -20 para obter -\frac{9}{5}.

$$\frac{9\sqrt{2}}{2}-\frac{16}{5}-\frac{9}{5}$$

Resta \frac{9}{5} de -\frac{16}{5} para obter -5.

$$\frac{9\sqrt{2}}{2}-5$$

Para sumar ou restar expresións, expándeas para facer que os seus denominadores sexan iguais. Multiplica 5 por \frac{2}{2}.

$$\frac{9\sqrt{2}}{2}-\frac{5\times 2}{2}$$

Dado que \frac{9\sqrt{2}}{2} e \frac{5\times 2}{2} teñen o mesmo denominador, réstaos mediante a resta dos seus numeradores.

$$\frac{9\sqrt{2}-5\times 2}{2}$$

Fai as multiplicacións en 9\sqrt{2}-5\times 2.

$$\frac{9\sqrt{2}-10}{2}$$

Factorizar

$$\frac{9 \sqrt{2} - 10}{2} = 1.3639610306789285$$