Pre-Algebra Examples

$\frac{2 x + 6}{2 x^{2} - 18} - \frac{2}{x - 3}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Cancel the common factor of $2 x + 6$ and $2 x^{2} - 18$ .

Tap for more steps...

Step 1.1.1

Factor $2$ out of $2 x$ .

$\frac{2 (x) + 6}{2 x^{2} - 18} - \frac{2}{x - 3}$

Step 1.1.2

Factor $2$ out of $6$ .

$\frac{2 (x) + 2 \cdot 3}{2 x^{2} - 18} - \frac{2}{x - 3}$

Step 1.1.3

Factor $2$ out of $2 (x) + 2 (3)$ .

$\frac{2 (x + 3)}{2 x^{2} - 18} - \frac{2}{x - 3}$

Step 1.1.4

Cancel the common factors.

Tap for more steps...

Step 1.1.4.1

Factor $2$ out of $2 x^{2}$ .

$\frac{2 (x + 3)}{2 (x^{2}) - 18} - \frac{2}{x - 3}$

Step 1.1.4.2

Factor $2$ out of $- 18$ .

$\frac{2 (x + 3)}{2 x^{2} + 2 \cdot - 9} - \frac{2}{x - 3}$

Step 1.1.4.3

Factor $2$ out of $2 x^{2} + 2 \cdot - 9$ .

$\frac{2 (x + 3)}{2 (x^{2} - 9)} - \frac{2}{x - 3}$

Step 1.1.4.4

Cancel the common factor.

$\frac{2 (x + 3)}{2 (x^{2} - 9)} - \frac{2}{x - 3}$

Step 1.1.4.5

Rewrite the expression.

$\frac{x + 3}{x^{2} - 9} - \frac{2}{x - 3}$

Step 1.2

Simplify the denominator.

Tap for more steps...

Step 1.2.1

Rewrite $9$ as $3^{2}$ .

$\frac{x + 3}{x^{2} - 3^{2}} - \frac{2}{x - 3}$

Step 1.2.2

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 $b = 3$ .

$\frac{x + 3}{(x + 3) (x - 3)} - \frac{2}{x - 3}$

Step 1.3

Cancel the common factor of $x + 3$ .

Tap for more steps...

Step 1.3.1

Cancel the common factor.

$\frac{x + 3}{(x + 3) (x - 3)} - \frac{2}{x - 3}$

Step 1.3.2

Rewrite the expression.

$\frac{1}{x - 3} - \frac{2}{x - 3}$

Step 2

Combine fractions.

Tap for more steps...

Step 2.1

Combine the numerators over the common denominator.

$\frac{1 - 2}{x - 3}$

Step 2.2

Simplify the expression.

Tap for more steps...

Step 2.2.1

Subtract $2$ from $1$ .

$\frac{- 1}{x - 3}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{1}{x - 3}$