Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

Step 1.2

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

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

Step 1.3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 x$ and $b = 1$ .

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

Step 2

Simplify terms.

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Step 2.1

Factor $2$ out of $4 x + 2$ .

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Step 2.1.1

Factor $2$ out of $4 x$ .

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

Step 2.1.2

Factor $2$ out of $2$ .

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

Step 2.1.3

Factor $2$ out of $2 (2 x) + 2 (1)$ .

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

Step 2.2

Cancel the common factor of $2 x + 1$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

$\frac{2 x - 1}{2}$