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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Since \frac{2a}{\left(a+b\right)\left(a-b\right)} and \frac{a-b}{\left(a+b\right)\left(a-b\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2a-\left(a-b\right).

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

Combine like terms in 2a-a+b.

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

Cancel out a+b in both numerator and denominator.

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

Differentiate w.r.t. a

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