Algebra Examples

$\frac{a^{2} - b^{2}}{a^{2} - a + a b - b}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

$\frac{(a + b) (a - b)}{a^{2} - a + a b - b}$

Step 2

Simplify the denominator.

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Step 2.1

Factor out the greatest common factor from each group.

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Step 2.1.1

Group the first two terms and the last two terms.

$\frac{(a + b) (a - b)}{(a^{2} - a) + a b - b}$

Step 2.1.2

Factor out the greatest common factor (GCF) from each group.

$\frac{(a + b) (a - b)}{a (a - 1) + b (a - 1)}$

Step 2.2

Factor the polynomial by factoring out the greatest common factor, $a - 1$ .

$\frac{(a + b) (a - b)}{(a - 1) (a + b)}$

Step 3

Cancel the common factor of $a + b$ .

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Step 3.1

Cancel the common factor.

$\frac{(a + b) (a - b)}{(a - 1) (a + b)}$

Step 3.2

Rewrite the expression.

$\frac{a - b}{a - 1}$