Algebra Examples

$f (x) = x^{2} - 1$ , $g (x) = x + 1$

Find the quotient of the functions.

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Replace the function designators with the actual functions in $\frac{f (x)}{g (x)}$ .

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

Simplify.

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Simplify the numerator.

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

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

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 $b = 1$ .

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

Cancel the common factor of $x + 1$ .

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Cancel the common factor.

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

Divide $x - 1$ by $1$ .

$x - 1$

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

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