Calculus Examples

$12 - \frac{192}{x^{2}}$

Step 1

To write $12$ as a fraction with a common denominator, multiply by $\frac{x^{2}}{x^{2}}$ .

$\frac{12 x^{2}}{x^{2}} - \frac{192}{x^{2}}$

Step 2

Combine the numerators over the common denominator.

$\frac{12 x^{2} - 192}{x^{2}}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $12$ out of $12 x^{2} - 192$ .

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Step 3.1.1

Factor $12$ out of $12 x^{2}$ .

$\frac{12 (x^{2}) - 192}{x^{2}}$

Step 3.1.2

Factor $12$ out of $- 192$ .

$\frac{12 x^{2} + 12 \cdot - 16}{x^{2}}$

Step 3.1.3

Factor $12$ out of $12 x^{2} + 12 \cdot - 16$ .

$\frac{12 (x^{2} - 16)}{x^{2}}$

Step 3.2

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

$\frac{12 (x^{2} - 4^{2})}{x^{2}}$

Step 3.3

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 $b = 4$ .

$\frac{12 (x + 4) (x - 4)}{x^{2}}$