Solve 8ab^2/ab^2-bdiv4ab/2-2ab

$$\frac { 8 a b ^ { 2 } } { a b ^ { 2 } - b } \div \frac { 4 a b } { 2 - 2 a b }$$

Evaluate

$$-4$$

Short Solution Steps

Divide \frac{8ab^{2}}{ab^{2}-b} by \frac{4ab}{2-2ab} by multiplying \frac{8ab^{2}}{ab^{2}-b} by the reciprocal of \frac{4ab}{2-2ab}.

$$\frac{8ab^{2}\left(2-2ab\right)}{\left(ab^{2}-b\right)\times 4ab}$$

Cancel out 4ab in both numerator and denominator.

$$\frac{2b\left(-2ab+2\right)}{ab^{2}-b}$$

Factor the expressions that are not already factored.

$$\frac{2^{2}b\left(-ab+1\right)}{b\left(ab-1\right)}$$

Extract the negative sign in -ab+1.

$$\frac{-2^{2}b\left(ab-1\right)}{b\left(ab-1\right)}$$

Cancel out b\left(ab-1\right) in both numerator and denominator.

$$-2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$-4$$

Factor

$$-4$$