Algebra Examples

f (x) = x^{2} - 4

$f (x) = x^{2} - 4$ ,

g (x) = x - 2

$g (x) = x - 2$

Step 1

Replace the function designators with the actual functions in

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

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

\frac{x^{2} - 4}{x - 2}

$\frac{x^{2} - 4}{x - 2}$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the numerator.

Tap for more steps...

Step 2.1.1

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 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 = 2

$b = 2$ .

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

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

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

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

Step 2.2

Cancel the common factor of

x - 2

$x - 2$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

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

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

Step 2.2.2

Divide

x + 2

$x + 2$ by

1

$1$ .

x + 2

$x + 2$

x + 2

$x + 2$

x + 2

$x + 2$

Enter YOUR Problem