Algebra Examples

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

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 $b = y$ .

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

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

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

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Step 2.1.1

Factor $- 1$ out of $y$ .

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

Step 2.1.2

Factor $- 1$ out of $- x$ .

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

Step 2.1.3

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

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

Step 2.1.4

Reorder terms.

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

Step 2.1.5

Cancel the common factor.

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

Step 2.1.6

Rewrite the expression.

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

Step 2.2

Move the negative in front of the fraction.

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