Simplify x/(x^2-y^2)+y/(x^2-y^2)

$\frac{x}{x^{2} - y^{2}} + \frac{y}{x^{2} - y^{2}}$

Step 1

Combine the numerators over the common denominator.

$\frac{x + y}{x^{2} - y^{2}}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

$\frac{x + y}{(x + y) (x - y)}$

Step 3

Cancel the common factor of $x + y$ .

Cancel the common factor.

$\frac{x + y}{(x + y) (x - y)}$

Rewrite the expression.

$\frac{1}{x - y}$