Algebra Examples

$\frac{1}{\sqrt{x} + \sqrt{x - 5}}$

Step 1

Multiply $\frac{1}{\sqrt{x} + \sqrt{x - 5}}$ by $\frac{\sqrt{x} - \sqrt{x - 5}}{\sqrt{x} - \sqrt{x - 5}}$ .

$\frac{1}{\sqrt{x} + \sqrt{x - 5}} \cdot \frac{\sqrt{x} - \sqrt{x - 5}}{\sqrt{x} - \sqrt{x - 5}}$

Step 2

Multiply $\frac{1}{\sqrt{x} + \sqrt{x - 5}}$ by $\frac{\sqrt{x} - \sqrt{x - 5}}{\sqrt{x} - \sqrt{x - 5}}$ .

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{\sqrt{x} - \sqrt{x - 5}}{5}$