Basic Math Examples

$\frac{2 p^{2} - p + 5}{3 p^{3} - 12 p}$

Step 1

Factor $3 p$ out of $3 p^{3} - 12 p$ .

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Step 1.1

Factor $3 p$ out of $3 p^{3}$ .

$\frac{2 p^{2} - p + 5}{3 p (p^{2}) - 12 p}$

Step 1.2

Factor $3 p$ out of $- 12 p$ .

$\frac{2 p^{2} - p + 5}{3 p (p^{2}) + 3 p (- 4)}$

Step 1.3

Factor $3 p$ out of $3 p (p^{2}) + 3 p (- 4)$ .

$\frac{2 p^{2} - p + 5}{3 p (p^{2} - 4)}$

Step 2

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

$\frac{2 p^{2} - p + 5}{3 p (p^{2} - 2^{2})}$

Step 3

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

$\frac{2 p^{2} - p + 5}{3 p (p + 2) (p - 2)}$