Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Divide $\sqrt{x} + \sqrt{x - 1}$ by $1$ .

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