Calculus Examples

$\frac{\sqrt{x + 1} - \sqrt{2 \cdot x}}{x^{2} - 1}$

Step 1

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

$\frac{\sqrt{x + 1} - \sqrt{2 \cdot x}}{x^{2} - 1^{2}}$

Step 2

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 $b = 1$ .

$\frac{\sqrt{x + 1} - \sqrt{2 x}}{(x + 1) (x - 1)}$