Calculus Examples

$1 - \frac{25}{x^{2}}$

Step 1

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

$1^{2} - \frac{25}{x^{2}}$

Step 2

Rewrite $\frac{25}{x^{2}}$ as ${(\frac{5}{x})}^{2}$ .

$1^{2} - {(\frac{5}{x})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = \frac{5}{x}$ .

$(1 + \frac{5}{x}) (1 - \frac{5}{x})$