Finite Math Examples

$\frac{x^{2} + 5 x - 6}{x^{2} - 9} + \frac{x^{2} - 2 x - 12}{x^{2} - 9}$

Step 1

Simplify terms.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{x^{2} + 5 x - 6 + x^{2} - 2 x - 12}{x^{2} - 9}$

Step 1.2

Add $x^{2}$ and $x^{2}$ .

$\frac{2 x^{2} + 5 x - 6 - 2 x - 12}{x^{2} - 9}$

Step 1.3

Subtract $2 x$ from $5 x$ .

$\frac{2 x^{2} + 3 x - 6 - 12}{x^{2} - 9}$

Step 1.4

Subtract $12$ from $- 6$ .

$\frac{2 x^{2} + 3 x - 18}{x^{2} - 9}$

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 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 $b = 3$ .

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