Solve 1/ab-b^2-1/a^2-ab

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

Evaluate

$$\frac{1}{ab}$$

Short Solution Steps

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

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

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{1}{b\left(a-b\right)} times \frac{a}{a}. Multiply \frac{1}{a\left(a-b\right)} times \frac{b}{b}.

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

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

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

Cancel out a-b in both numerator and denominator.

$$\frac{1}{ab}$$

Differentiate w.r.t. a

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