Pre-Algebra Examples

$f (x) = \frac{x}{2 x + 22} - \frac{121}{x^{2} - 121}$

Step 1

Rewrite the function as an equation.

$y = \frac{x}{2 x + 22} - \frac{121}{x^{2} - 121}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Factor $2$ out of $2 x + 22$ .

Tap for more steps...

Step 2.1.1

Factor $2$ out of $2 x$ .

$y = \frac{x}{2 (x) + 22} - \frac{121}{x^{2} - 121}$

Step 2.1.2

Factor $2$ out of $22$ .

$y = \frac{x}{2 x + 2 \cdot 11} - \frac{121}{x^{2} - 121}$

Step 2.1.3

Factor $2$ out of $2 x + 2 \cdot 11$ .

$y = \frac{x}{2 (x + 11)} - \frac{121}{x^{2} - 121}$

Step 2.2

Simplify the denominator.

Tap for more steps...

Step 2.2.1

Rewrite $121$ as $11^{2}$ .

$y = \frac{x}{2 (x + 11)} - \frac{121}{x^{2} - 11^{2}}$

Step 2.2.2

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 $b = 11$ .

$y = \frac{x}{2 (x + 11)} - \frac{121}{(x + 11) (x - 11)}$