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

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

Evaluate

$$-\frac{17}{8}=-2.125$$

Solution Steps

Add \frac{2}{3} and \frac{1}{4} to get \frac{11}{12}.

$$\left(\frac{\frac{1}{4}-\frac{11}{12}}{1+\frac{1}{1+\frac{7}{5}}}\right)^{-1}$$

Subtract \frac{11}{12} from \frac{1}{4} to get -\frac{2}{3}.

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

Add 1 and \frac{7}{5} to get \frac{12}{5}.

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

Divide 1 by \frac{12}{5} by multiplying 1 by the reciprocal of \frac{12}{5}.

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

Multiply 1 and \frac{5}{12} to get \frac{5}{12}.

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

Add 1 and \frac{5}{12} to get \frac{17}{12}.

$$\left(\frac{-\frac{2}{3}}{\frac{17}{12}}\right)^{-1}$$

Divide -\frac{2}{3} by \frac{17}{12} by multiplying -\frac{2}{3} by the reciprocal of \frac{17}{12}.

$$\left(-\frac{2}{3}\times \frac{12}{17}\right)^{-1}$$

Multiply -\frac{2}{3} and \frac{12}{17} to get -\frac{8}{17}.

$$\left(-\frac{8}{17}\right)^{-1}$$

Calculate -\frac{8}{17} to the power of -1 and get -\frac{17}{8}.

$$-\frac{17}{8}$$

Factor

$$-\frac{17}{8} = -2\frac{1}{8} = -2.125$$