Trigonometry Examples

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

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 $x - y$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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