Algebra Examples

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

Step 1

Combine the numerators over the common denominator.

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

Step 2

Simplify the numerator.

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Step 2.1

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

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

Step 2.2

Reorder $- 3^{2}$ and $x^{2}$ .

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

Step 2.3

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 $b = 3$ .

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

Step 3

Cancel the common factor of $x + 3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Divide $x - 3$ by $1$ .

$x - 3$