Solve 2ab/a^{2-b^{2}}+a^2+b^2/a^2-b^2

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

Evaluate

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

Short Solution Steps

Since \frac{2ab}{a^{2}-b^{2}} and \frac{a^{2}+b^{2}}{a^{2}-b^{2}} have the same denominator, add them by adding their numerators.

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

Factor the expressions that are not already factored in \frac{2ab+a^{2}+b^{2}}{a^{2}-b^{2}}.

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

Cancel out a+b in both numerator and denominator.

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

Expand

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

Short Solution Steps

Since \frac{2ab}{a^{2}-b^{2}} and \frac{a^{2}+b^{2}}{a^{2}-b^{2}} have the same denominator, add them by adding their numerators.

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

Factor the expressions that are not already factored in \frac{2ab+a^{2}+b^{2}}{a^{2}-b^{2}}.

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

Cancel out a+b in both numerator and denominator.

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