Solve (3/4a^2b^2-1/4a^2b^2):(-5ab+2ab)

$$( \frac { 3 } { 4 } a ^ { 2 } b ^ { 2 } - \frac { 1 } { 4 } a ^ { 2 } b ^ { 2 } ) : ( - 5 a b + 2 a b )$$

Evaluate

$$-\frac{ab}{6}$$

Solution Steps

Combine \frac{3}{4}a^{2}b^{2} and -\frac{1}{4}a^{2}b^{2} to get \frac{1}{2}a^{2}b^{2}.

$$\frac{\frac{1}{2}a^{2}b^{2}}{-5ab+2ab}$$

Combine -5ab and 2ab to get -3ab.

$$\frac{\frac{1}{2}a^{2}b^{2}}{-3ab}$$

Cancel out ab in both numerator and denominator.

$$\frac{\frac{1}{2}ab}{-3}$$

Divide \frac{1}{2}ab by -3 to get -\frac{1}{6}ab.

$$-\frac{1}{6}ab$$

Expand

$$-\frac{ab}{6}$$

Solution Steps

Combine \frac{3}{4}a^{2}b^{2} and -\frac{1}{4}a^{2}b^{2} to get \frac{1}{2}a^{2}b^{2}.

$$\frac{\frac{1}{2}a^{2}b^{2}}{-5ab+2ab}$$

Combine -5ab and 2ab to get -3ab.

$$\frac{\frac{1}{2}a^{2}b^{2}}{-3ab}$$

Cancel out ab in both numerator and denominator.

$$\frac{\frac{1}{2}ab}{-3}$$

Divide \frac{1}{2}ab by -3 to get -\frac{1}{6}ab.

$$-\frac{1}{6}ab$$