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

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

Evaluate

$$-\frac{1}{14}\approx -0.071428571$$

Solution Steps

Subtract 2 from \frac{5}{6} to get -\frac{7}{6}.

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

Calculate -\frac{7}{6} to the power of -1 and get -\frac{6}{7}.

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

Subtract \frac{4}{3} from \frac{5}{2} to get \frac{7}{6}.

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

Calculate \frac{7}{6} to the power of -2 and get \frac{36}{49}.

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

Add -\frac{6}{7} and \frac{36}{49} to get -\frac{6}{49}.

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

Calculate \frac{12}{7} to the power of -1 and get \frac{7}{12}.

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

Multiply -\frac{6}{49} and \frac{7}{12} to get -\frac{1}{14}.

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

Factor

$$-\frac{1}{14} = -0.07142857142857142$$