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

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

Step 1

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 $b = y$ .

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

Step 2

Simplify terms.

Cancel the common factor of $x - y$ and $y - x$ .

Factor $- 1$ out of $x$ .

$\frac{(x + y) (- 1 (- x) - y)}{y - x}$

Factor $- 1$ out of $- y$ .

$\frac{(x + y) (- 1 (- x) - (y))}{y - x}$

Factor $- 1$ out of $- 1 (- x) - (y)$ .

$\frac{(x + y) (- 1 (- x + y))}{y - x}$

Reorder terms.

$\frac{(x + y) (- 1 (- x + y))}{- x + y}$

Cancel the common factor.

$\frac{(x + y) (- 1 (- x + y))}{- x + y}$

Divide $(x + y) \cdot (- 1)$ by $1$ .

$(x + y) \cdot (- 1)$

Simplify by multiplying through.

Apply the distributive property.

$x \cdot - 1 + y \cdot - 1$

Reorder.

Move $- 1$ to the left of $x$ .

$- 1 \cdot x + y \cdot - 1$

Move $- 1$ to the left of $y$ .

$- 1 \cdot x - 1 \cdot y$

Simplify each term.

Rewrite $- 1 x$ as $- x$ .

$- x - 1 \cdot y$

Rewrite $- 1 y$ as $- y$ .

$- x - y$