Algebra Examples

$\frac{8}{x + 7} - \frac{7 x}{x^{2} - 49}$

Step 1

Simplify the denominator.

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Step 1.1

Rewrite $49$ as $7^{2}$ .

$\frac{8}{x + 7} - \frac{7 x}{x^{2} - 7^{2}}$

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 $b = 7$ .

$\frac{8}{x + 7} - \frac{7 x}{(x + 7) (x - 7)}$

Step 2

To write $\frac{8}{x + 7}$ as a fraction with a common denominator, multiply by $\frac{x - 7}{x - 7}$ .

$\frac{8}{x + 7} \cdot \frac{x - 7}{x - 7} - \frac{7 x}{(x + 7) (x - 7)}$

Step 3

Simplify terms.

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Step 3.1

Multiply $\frac{8}{x + 7}$ by $\frac{x - 7}{x - 7}$ .

$\frac{8 (x - 7)}{(x + 7) (x - 7)} - \frac{7 x}{(x + 7) (x - 7)}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{8 (x - 7) - 7 x}{(x + 7) (x - 7)}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{8 x + 8 \cdot - 7 - 7 x}{(x + 7) (x - 7)}$

Step 4.2

Multiply $8$ by $- 7$ .

$\frac{8 x - 56 - 7 x}{(x + 7) (x - 7)}$

Step 4.3

Subtract $7 x$ from $8 x$ .

$\frac{x - 56}{(x + 7) (x - 7)}$