Solve (-3/2+1/2)^3-3/9/-1/9+4/3+-3/2-6/9

$$\frac { ( - 3 / 2 + 1 / 2 ) ^ { 3 } - 3 / 9 } { - 1 / 9 + 4 / 3 + - 3 / 2 - 6 / 9 }$$

Evaluate

$$\frac{24}{17}\approx 1.411764706$$

Solution Steps

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

$$\frac{\left(-1\right)^{3}-\frac{3}{9}}{-\frac{1}{9}+\frac{4}{3}-\frac{3}{2}-\frac{6}{9}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{-1-\frac{3}{9}}{-\frac{1}{9}+\frac{4}{3}-\frac{3}{2}-\frac{6}{9}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{-1-\frac{1}{3}}{-\frac{1}{9}+\frac{4}{3}-\frac{3}{2}-\frac{6}{9}}$$

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

$$\frac{-\frac{4}{3}}{-\frac{1}{9}+\frac{4}{3}-\frac{3}{2}-\frac{6}{9}}$$

Add -\frac{1}{9} and \frac{4}{3} to get \frac{11}{9}.

$$\frac{-\frac{4}{3}}{\frac{11}{9}-\frac{3}{2}-\frac{6}{9}}$$

Subtract \frac{3}{2} from \frac{11}{9} to get -\frac{5}{18}.

$$\frac{-\frac{4}{3}}{-\frac{5}{18}-\frac{6}{9}}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{4}{3}}{-\frac{5}{18}-\frac{2}{3}}$$

Subtract \frac{2}{3} from -\frac{5}{18} to get -\frac{17}{18}.

$$\frac{-\frac{4}{3}}{-\frac{17}{18}}$$

Divide -\frac{4}{3} by -\frac{17}{18} by multiplying -\frac{4}{3} by the reciprocal of -\frac{17}{18}.

$$-\frac{4}{3}\left(-\frac{18}{17}\right)$$

Multiply -\frac{4}{3} and -\frac{18}{17} to get \frac{24}{17}.

$$\frac{24}{17}$$

Factor

$$\frac{2 ^ {3} \cdot 3}{17} = 1\frac{7}{17} = 1.411764705882353$$