Solve 5/a+b+3/a-b

$$\frac { 5 } { a + b } + \frac { 3 } { a - b }$$

Evaluate

$$\frac{2\left(4a-b\right)}{a^{2}-b^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a+b and a-b is \left(a+b\right)\left(a-b\right). Multiply \frac{5}{a+b} times \frac{a-b}{a-b}. Multiply \frac{3}{a-b} times \frac{a+b}{a+b}.

$$\frac{5\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}+\frac{3\left(a+b\right)}{\left(a+b\right)\left(a-b\right)}$$

Since \frac{5\left(a-b\right)}{\left(a+b\right)\left(a-b\right)} and \frac{3\left(a+b\right)}{\left(a+b\right)\left(a-b\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\left(a-b\right)+3\left(a+b\right)}{\left(a+b\right)\left(a-b\right)}$$

Do the multiplications in 5\left(a-b\right)+3\left(a+b\right).

$$\frac{5a-5b+3a+3b}{\left(a+b\right)\left(a-b\right)}$$

Combine like terms in 5a-5b+3a+3b.

$$\frac{8a-2b}{\left(a+b\right)\left(a-b\right)}$$

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

$$\frac{8a-2b}{a^{2}-b^{2}}$$

Differentiate w.r.t. a

$$\frac{4\left(-2a^{2}+ab-2b^{2}\right)}{\left(a^{2}-b^{2}\right)^{2}}$$