Solve 11/7:[(-3/2)^-1-(4/3-2)^2*(3/7-frac{3}{4})]

$$\frac { 11 } { 7 } : [ ( - \frac { 3 } { 2 } ) ^ { - 1 } - ( \frac { 4 } { 3 } - 2 ) ^ { 2 } \cdot ( \frac { 3 } { 7 } - \frac { 3 } { 4 } ) ]$$

Evaluate

$$-3$$

Solution Steps

Calculate -\frac{3}{2} to the power of -1 and get -\frac{2}{3}.

$$\frac{\frac{11}{7}}{-\frac{2}{3}-\left(\frac{4}{3}-2\right)^{2}\left(\frac{3}{7}-\frac{3}{4}\right)}$$

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

$$\frac{\frac{11}{7}}{-\frac{2}{3}-\left(-\frac{2}{3}\right)^{2}\left(\frac{3}{7}-\frac{3}{4}\right)}$$

Calculate -\frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{\frac{11}{7}}{-\frac{2}{3}-\frac{4}{9}\left(\frac{3}{7}-\frac{3}{4}\right)}$$

Subtract \frac{3}{4} from \frac{3}{7} to get -\frac{9}{28}.

$$\frac{\frac{11}{7}}{-\frac{2}{3}-\frac{4}{9}\left(-\frac{9}{28}\right)}$$

Multiply \frac{4}{9} and -\frac{9}{28} to get -\frac{1}{7}.

$$\frac{\frac{11}{7}}{-\frac{2}{3}-\left(-\frac{1}{7}\right)}$$

The opposite of -\frac{1}{7} is \frac{1}{7}.

$$\frac{\frac{11}{7}}{-\frac{2}{3}+\frac{1}{7}}$$

Add -\frac{2}{3} and \frac{1}{7} to get -\frac{11}{21}.

$$\frac{\frac{11}{7}}{-\frac{11}{21}}$$

Divide \frac{11}{7} by -\frac{11}{21} by multiplying \frac{11}{7} by the reciprocal of -\frac{11}{21}.

$$\frac{11}{7}\left(-\frac{21}{11}\right)$$

Multiply \frac{11}{7} and -\frac{21}{11} to get -3.

$$-3$$

Factor

$$-3$$