Solve (-2a^{2}b^{2}+5a^{2}b^{2}-6a^2b^2):(-1/2a^2b+1/6a^2b)

$$( - 2 a ^ { 2 } b ^ { 2 } + 5 a ^ { 2 } b ^ { 2 } - 6 a ^ { 2 } b ^ { 2 } ) : ( - \frac { 1 } { 2 } a ^ { 2 } b + \frac { 1 } { 6 } a ^ { 2 } b )$$

Evaluate

$$9b$$

Solution Steps

Combine -2a^{2}b^{2} and 5a^{2}b^{2} to get 3a^{2}b^{2}.

$$\frac{3a^{2}b^{2}-6a^{2}b^{2}}{-\frac{1}{2}a^{2}b+\frac{1}{6}a^{2}b}$$

Combine 3a^{2}b^{2} and -6a^{2}b^{2} to get -3a^{2}b^{2}.

$$\frac{-3a^{2}b^{2}}{-\frac{1}{2}a^{2}b+\frac{1}{6}a^{2}b}$$

Combine -\frac{1}{2}a^{2}b and \frac{1}{6}a^{2}b to get -\frac{1}{3}a^{2}b.

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

Cancel out ba^{2} in both numerator and denominator.

$$\frac{-3b}{-\frac{1}{3}}$$

Divide -3b by -\frac{1}{3} by multiplying -3b by the reciprocal of -\frac{1}{3}.

$$\frac{-3b\times 3}{-1}$$

Multiply -3 and 3 to get -9.

$$\frac{-9b}{-1}$$

Anything divided by -1 gives its opposite.

$$9b$$

Expand

$$9b$$

Solution Steps

Combine -2a^{2}b^{2} and 5a^{2}b^{2} to get 3a^{2}b^{2}.

$$\frac{3a^{2}b^{2}-6a^{2}b^{2}}{-\frac{1}{2}a^{2}b+\frac{1}{6}a^{2}b}$$

Combine 3a^{2}b^{2} and -6a^{2}b^{2} to get -3a^{2}b^{2}.

$$\frac{-3a^{2}b^{2}}{-\frac{1}{2}a^{2}b+\frac{1}{6}a^{2}b}$$

Combine -\frac{1}{2}a^{2}b and \frac{1}{6}a^{2}b to get -\frac{1}{3}a^{2}b.

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

Cancel out ba^{2} in both numerator and denominator.

$$\frac{-3b}{-\frac{1}{3}}$$

Divide -3b by -\frac{1}{3} by multiplying -3b by the reciprocal of -\frac{1}{3}.

$$\frac{-3b\times 3}{-1}$$

Multiply -3 and 3 to get -9.

$$\frac{-9b}{-1}$$

Anything divided by -1 gives its opposite.

$$9b$$