Algebra Examples

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

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

g (x) = x + 1

$g (x) = x + 1$

Step 1

Find the quotient of the functions.

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Step 1.1

Replace the function designators with the actual functions in

\frac{f (x)}{g (x)}

$\frac{f (x)}{g (x)}$ .

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

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

Step 1.2

Simplify.

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Step 1.2.1

Simplify the numerator.

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Step 1.2.1.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

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

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

Step 1.2.1.2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = x

$a = x$ and

b = 1

$b = 1$ .

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

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

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

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

Step 1.2.2

Cancel the common factor of

x + 1

$x + 1$ .

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Step 1.2.2.1

Cancel the common factor.

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

Step 1.2.2.2

Divide

$x - 1$ by

$1$ .

$x - 1$

Step 2

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:

${x | x \in ℝ}$

Step 3

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