Resolver left({left(5/6-2right)}^-1+{left(5/2-4/3right)}^-2right){left(12/7right)}^-1

$$\left( { \left( \frac{ 5 }{ 6 } -2 \right) }^{ -1 } + { \left( \frac{ 5 }{ 2 } - \frac{ 4 }{ 3 } \right) }^{ -2 } \right) { \left( \frac{ 12 }{ 7 } \right) }^{ -1 }$$

Avaliar

$$-\frac{1}{14}\approx -0,071428571$$

Passos Para a Resolução

Subtraia 2 de \frac{5}{6} para obter -\frac{7}{6}.

$$\left(\left(-\frac{7}{6}\right)^{-1}+\left(\frac{5}{2}-\frac{4}{3}\right)^{-2}\right)\times \left(\frac{12}{7}\right)^{-1}$$

Calcule -\frac{7}{6} elevado a -1 e obtenha -\frac{6}{7}.

$$\left(-\frac{6}{7}+\left(\frac{5}{2}-\frac{4}{3}\right)^{-2}\right)\times \left(\frac{12}{7}\right)^{-1}$$

Subtraia \frac{4}{3} de \frac{5}{2} para obter \frac{7}{6}.

$$\left(-\frac{6}{7}+\left(\frac{7}{6}\right)^{-2}\right)\times \left(\frac{12}{7}\right)^{-1}$$

Calcule \frac{7}{6} elevado a -2 e obtenha \frac{36}{49}.

$$\left(-\frac{6}{7}+\frac{36}{49}\right)\times \left(\frac{12}{7}\right)^{-1}$$

Some -\frac{6}{7} e \frac{36}{49} para obter -\frac{6}{49}.

$$-\frac{6}{49}\times \left(\frac{12}{7}\right)^{-1}$$

Calcule \frac{12}{7} elevado a -1 e obtenha \frac{7}{12}.

$$-\frac{6}{49}\times \frac{7}{12}$$

Multiplique -\frac{6}{49} e \frac{7}{12} para obter -\frac{1}{14}.

$$-\frac{1}{14}$$

Fatorizar

$$-\frac{1}{14} = -0,07142857142857142$$