Solve 1/a-b+e/a^2-b^2=

$$\frac { 1 } { a - b } + \frac { e } { a ^ { 2 } - b ^ { 2 } } =$$

Evaluate

$$\frac{a+b+e}{a^{2}-b^{2}}$$

Short Solution Steps

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a-b and \left(a+b\right)\left(a-b\right) is \left(a+b\right)\left(a-b\right). Multiply \frac{1}{a-b} times \frac{a+b}{a+b}.

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

Since \frac{a+b}{\left(a+b\right)\left(a-b\right)} and \frac{e}{\left(a+b\right)\left(a-b\right)} have the same denominator, add them by adding their numerators.

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

Expand \left(a+b\right)\left(a-b\right).

$$\frac{a+b+e}{a^{2}-b^{2}}$$

Differentiate w.r.t. a

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