Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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 $b = y$ .

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

Step 1.2

Cancel the common factor of $x - y$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Divide $x + y$ by $1$ .

$x + y - (x + y)$

Step 1.3

Apply the distributive property.

$x + y - x - y$

Step 2

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

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Step 2.1

Subtract $x$ from $x$ .

$y + 0 - y$

Step 2.2

Add $y$ and $0$ .

$y - y$

Step 2.3

Subtract $y$ from $y$ .

$0$