Algebra Examples

$\frac{x}{x + 3} - \frac{6 x}{x^{2} - 9}$

Step 1

Simplify the denominator.

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Step 1.1

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

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

Step 1.2

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 $b = 3$ .

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

Step 2

To write $\frac{x}{x + 3}$ as a fraction with a common denominator, multiply by $\frac{x - 3}{x - 3}$ .

$\frac{x}{x + 3} \cdot \frac{x - 3}{x - 3} - \frac{6 x}{(x + 3) (x - 3)}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{x}{x + 3}$ by $\frac{x - 3}{x - 3}$ .

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Factor $x$ out of $x (x - 3) - 6 x$ .

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Step 4.1.1

Factor $x$ out of $- 6 x$ .

$\frac{x (x - 3) + x \cdot - 6}{(x + 3) (x - 3)}$

Step 4.1.2

Factor $x$ out of $x (x - 3) + x \cdot - 6$ .

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

Step 4.2

Subtract $6$ from $- 3$ .

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