Pre-Algebra Examples

$(x^{2} - 1) \div (x - 1)$

Step 1

Rewrite the division as a fraction.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

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 $b = 1$ .

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

Step 3

Cancel the common factor of $x - 1$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $x + 1$ by $1$ .

$x + 1$