Basic Math Examples

$\frac{s^{4}}{s^{4} - 1}$

Step 1

Rewrite $s^{4}$ as ${(s^{2})}^{2}$ .

$\frac{s^{4}}{{(s^{2})}^{2} - 1}$

Step 2

Rewrite $1$ as $1^{2}$ .

$\frac{s^{4}}{{(s^{2})}^{2} - 1^{2}}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = s^{2}$ and $b = 1$ .

$\frac{s^{4}}{(s^{2} + 1) (s^{2} - 1)}$

Step 4

Simplify.

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Step 4.1

Rewrite $1$ as $1^{2}$ .

$\frac{s^{4}}{(s^{2} + 1) (s^{2} - 1^{2})}$

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = s$ and $b = 1$ .

$\frac{s^{4}}{(s^{2} + 1) (s + 1) (s - 1)}$