Linear Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

$\frac{\sqrt{x} - \sqrt{y}}{{\sqrt{x}}^{2} - \sqrt{x y} + \sqrt{y x} - {\sqrt{y}}^{2}}$

Step 4

Simplify.

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