Solve (-2/3-3/2)div(-3/2+2/3)

$$( - \frac { 2 } { 3 } - \frac { 3 } { 2 } ) \div ( - \frac { 3 } { 2 } + \frac { 2 } { 3 } )$$

Evaluate

$$\frac{13}{5}=2.6$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{3}{2} to fractions with denominator 6.

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

Since -\frac{4}{6} and \frac{9}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 9 from -4 to get -13.

$$\frac{-\frac{13}{6}}{-\frac{3}{2}+\frac{2}{3}}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{-\frac{13}{6}}{-\frac{9}{6}+\frac{4}{6}}$$

Since -\frac{9}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{-\frac{13}{6}}{\frac{-9+4}{6}}$$

Add -9 and 4 to get -5.

$$\frac{-\frac{13}{6}}{-\frac{5}{6}}$$

Divide -\frac{13}{6} by -\frac{5}{6} by multiplying -\frac{13}{6} by the reciprocal of -\frac{5}{6}.

$$-\frac{13}{6}\left(-\frac{6}{5}\right)$$

Multiply -\frac{13}{6} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13\left(-6\right)}{6\times 5}$$

Do the multiplications in the fraction \frac{-13\left(-6\right)}{6\times 5}.

$$\frac{78}{30}$$

Reduce the fraction \frac{78}{30} to lowest terms by extracting and canceling out 6.

$$\frac{13}{5}$$

Factor

$$\frac{13}{5} = 2\frac{3}{5} = 2.6$$