Solve (1+1/2+1/3/1-frac{1{2}-1/3})^-1

$$( \frac { 1 + \frac { 1 } { 2 } + \frac { 1 } { 3 } } { 1 - \frac { 1 } { 2 } - \frac { 1 } { 3 } } ) ^ { - 1 }$$

Evaluate

$$\frac{1}{11}\approx 0.090909091$$

Solution Steps

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

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

Add \frac{3}{2} and \frac{1}{3} to get \frac{11}{6}.

$$\left(\frac{\frac{11}{6}}{1-\frac{1}{2}-\frac{1}{3}}\right)^{-1}$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\left(\frac{\frac{11}{6}}{\frac{1}{2}-\frac{1}{3}}\right)^{-1}$$

Subtract \frac{1}{3} from \frac{1}{2} to get \frac{1}{6}.

$$\left(\frac{\frac{11}{6}}{\frac{1}{6}}\right)^{-1}$$

Divide \frac{11}{6} by \frac{1}{6} by multiplying \frac{11}{6} by the reciprocal of \frac{1}{6}.

$$\left(\frac{11}{6}\times 6\right)^{-1}$$

Multiply \frac{11}{6} and 6 to get 11.

$$11^{-1}$$

Calculate 11 to the power of -1 and get \frac{1}{11}.

$$\frac{1}{11}$$

Factor

$$\frac{1}{11} = 0.09090909090909091$$