Solve a/ab+b^2-b/a^2+ab)*ab^2/a-b

$$\frac { a } { a b + b ^ { 2 } } - \frac { b } { a ^ { 2 } + a b } ) \cdot \frac { a b ^ { 2 } } { a - b }$$

Evaluate

$$\frac{a-b}{ab}$$

Short Solution Steps

Factor ab+b^{2}. Factor a^{2}+ab.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b\left(a+b\right) and a\left(a+b\right) is ab\left(a+b\right). Multiply \frac{a}{b\left(a+b\right)} times \frac{a}{a}. Multiply \frac{b}{a\left(a+b\right)} times \frac{b}{b}.

$$\frac{aa}{ab\left(a+b\right)}-\frac{bb}{ab\left(a+b\right)}$$

Since \frac{aa}{ab\left(a+b\right)} and \frac{bb}{ab\left(a+b\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{aa-bb}{ab\left(a+b\right)}$$

Do the multiplications in aa-bb.

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

Factor the expressions that are not already factored in \frac{a^{2}-b^{2}}{ab\left(a+b\right)}.

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

Cancel out a+b in both numerator and denominator.

$$\frac{a-b}{ab}$$

Differentiate w.r.t. b

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