Finite Math Examples

$\frac{\frac{x^{2} - 16}{3 x^{2}}}{x - 4}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{2} - 16}{3 x^{2}} \cdot \frac{1}{x - 4}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$\frac{x^{2} - 4^{2}}{3 x^{2}} \cdot \frac{1}{x - 4}$

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 $b = 4$ .

$\frac{(x + 4) (x - 4)}{3 x^{2}} \cdot \frac{1}{x - 4}$

Step 3

Cancel the common factor of $x - 4$ .

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Step 3.1

Factor $x - 4$ out of $(x + 4) (x - 4)$ .

$\frac{(x - 4) (x + 4)}{3 x^{2}} \cdot \frac{1}{x - 4}$

Step 3.2

Cancel the common factor.

$\frac{(x - 4) (x + 4)}{3 x^{2}} \cdot \frac{1}{x - 4}$

Step 3.3

Rewrite the expression.

$\frac{x + 4}{3 x^{2}}$