Precalculus Examples

$\frac{4 (x^{2} - 1)}{12 (x + 2) (x - 1)}$

Step 1

Cancel the common factors.

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Step 1.1

Factor $4$ out of $12 (x + 2) (x - 1)$ .

$\frac{4 (x^{2} - 1)}{4 (3 (x + 2) (x - 1))}$

Step 1.2

Cancel the common factor.

$\frac{4 (x^{2} - 1)}{4 (3 (x + 2) (x - 1))}$

Step 1.3

Rewrite the expression.

$\frac{x^{2} - 1}{3 (x + 2) (x - 1)}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $1$ as $1^{2}$ .

$\frac{x^{2} - 1^{2}}{3 (x + 2) (x - 1)}$

Step 2.2

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 $b = 1$ .

$\frac{(x + 1) (x - 1)}{3 (x + 2) (x - 1)}$

Step 3

Cancel the common factor of $x - 1$ .

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Step 3.1

Cancel the common factor.

$\frac{(x + 1) (x - 1)}{3 (x + 2) (x - 1)}$

Step 3.2

Rewrite the expression.

$\frac{x + 1}{3 (x + 2)}$