Solve [(3/6-1/3)*(4/5+frac{1/3)^-1}{(frac{3}{4}+frac{1}{3}-frac{1}{6}+frac{1}{3})^-1}]=

$$[ \frac { ( \frac { 3 } { 6 } - \frac { 1 } { 3 } ) \cdot ( \frac { 4 } { 5 } + \frac { 1 } { 3 } ) ^ { - 1 } } { ( \frac { 3 } { 4 } + \frac { 1 } { 3 } - \frac { 1 } { 6 } + \frac { 1 } { 3 } ) ^ { - 1 } } ] =$$

Evaluate

$$\frac{25}{136}\approx 0.183823529$$

Solution Steps

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

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

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

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

Add \frac{4}{5} and \frac{1}{3} to get \frac{17}{15}.

$$\frac{\frac{1}{6}\times \left(\frac{17}{15}\right)^{-1}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Calculate \frac{17}{15} to the power of -1 and get \frac{15}{17}.

$$\frac{\frac{1}{6}\times \frac{15}{17}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Multiply \frac{1}{6} and \frac{15}{17} to get \frac{5}{34}.

$$\frac{\frac{5}{34}}{\left(\frac{3}{4}+\frac{1}{3}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Add \frac{3}{4} and \frac{1}{3} to get \frac{13}{12}.

$$\frac{\frac{5}{34}}{\left(\frac{13}{12}-\frac{1}{6}+\frac{1}{3}\right)^{-1}}$$

Subtract \frac{1}{6} from \frac{13}{12} to get \frac{11}{12}.

$$\frac{\frac{5}{34}}{\left(\frac{11}{12}+\frac{1}{3}\right)^{-1}}$$

Add \frac{11}{12} and \frac{1}{3} to get \frac{5}{4}.

$$\frac{\frac{5}{34}}{\left(\frac{5}{4}\right)^{-1}}$$

Calculate \frac{5}{4} to the power of -1 and get \frac{4}{5}.

$$\frac{\frac{5}{34}}{\frac{4}{5}}$$

Divide \frac{5}{34} by \frac{4}{5} by multiplying \frac{5}{34} by the reciprocal of \frac{4}{5}.

$$\frac{5}{34}\times \frac{5}{4}$$

Multiply \frac{5}{34} and \frac{5}{4} to get \frac{25}{136}.

$$\frac{25}{136}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {3} \cdot 17} = 0.18382352941176472$$