Algebra Examples

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

Distribute the value across the operation.

$f (x) \div g x$

Evaluate $f (x)$ .

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Replace the variable $x$ with $x$ in the expression.

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

Simplify the result.

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Remove parentheses around $x$ .

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

The final answer is $x^{2} - 1$ .

$x^{2} - 1$

Evaluate $g (x)$ .

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Replace the variable $x$ with $x$ in the expression.

$g (x) = (x) + 1$

Simplify the result.

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Remove parentheses around $x$ .

$g (x) = x + 1$

The final answer is $x + 1$ .

$x + 1$

Compose the result function for $f (x) \div g x$ by replacing the function designators with the actual functions.

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

Simplify.

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Rewrite the division as a fraction.

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

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 $b = 1$ .

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

Reduce the expression by cancelling the common factors.

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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.

$(- \infty, \infty)$

${x | x \in ℝ}$

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