Calculus Examples

$\frac{- 12 x^{2} + 48}{{(x^{2} + 4)}^{2}}$

Step 1

Factor $12$ out of $- 12 x^{2} + 48$ .

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Step 1.1

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

$\frac{12 (- x^{2}) + 48}{{(x^{2} + 4)}^{2}}$

Step 1.2

Factor $12$ out of $48$ .

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

Step 1.3

Factor $12$ out of $12 (- x^{2}) + 12 (4)$ .

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

Step 2

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

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

Step 3

Reorder $- x^{2}$ and $2^{2}$ .

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

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = x$ .

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