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

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

Step 1

Simplify each term.

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 $b = y$ .

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

Cancel the common factor of $x - y$ .

Cancel the common factor.

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

Divide $x + y$ by $1$ .

$x + y - (x + y)$

Apply the distributive property.

$x + y - x - y$

Step 2

Combine the opposite terms in $x + y - x - y$ .

Subtract $x$ from $x$ .

$y + 0 - y$

Add $y$ and $0$ .

$y - y$

Subtract $y$ from $y$ .

$0$