Solve (-2ab)divab^2/a-b*1/2(b-a)^2

$$( - 2 a b ) \div \frac { a b ^ { 2 } } { a - b } \times \frac { 1 } { 2 ( b - a ) ^ { 2 } }$$

Evaluate

$$\frac{1}{b\left(b-a\right)}$$

Solution Steps

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

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

Cancel out ab in both numerator and denominator.

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

Multiply \frac{-2\left(a-b\right)}{b} times \frac{1}{2\left(b-a\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(a-b\right)}{b\times 2\left(b-a\right)^{2}}$$

Cancel out 2 in both numerator and denominator.

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

To find the opposite of a-b, find the opposite of each term.

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

Cancel out -a+b in both numerator and denominator.

$$\frac{1}{b\left(-a+b\right)}$$

Use the distributive property to multiply b by -a+b.

$$\frac{1}{-ba+b^{2}}$$

Expand

$$\frac{1}{b\left(b-a\right)}$$

Solution Steps

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

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

Cancel out ab in both numerator and denominator.

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

Multiply \frac{-2\left(a-b\right)}{b} times \frac{1}{2\left(b-a\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\left(a-b\right)}{b\times 2\left(b-a\right)^{2}}$$

Cancel out 2 in both numerator and denominator.

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

To find the opposite of a-b, find the opposite of each term.

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

Cancel out -a+b in both numerator and denominator.

$$\frac{1}{b\left(-a+b\right)}$$

Use the distributive property to multiply b by -a+b.

$$\frac{1}{-ba+b^{2}}$$