Solve a/a+b+b/a-b

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

Evaluate

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

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{a}{a+b} times \frac{a-b}{a-b}. Multiply \frac{b}{a-b} times \frac{a+b}{a+b}.

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

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

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

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

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

Combine like terms in a^{2}-ab+ba+b^{2}.

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

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

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

Differentiate w.r.t. a

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