Algebra Examples

$\frac{x}{\sqrt{5} - \sqrt{3}}$

Step 1

Multiply $\frac{x}{\sqrt{5} - \sqrt{3}}$ by $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ .

$\frac{x}{\sqrt{5} - \sqrt{3}} \cdot \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}}$

Step 2

Multiply $\frac{x}{\sqrt{5} - \sqrt{3}}$ by $\frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ .

$\frac{x (\sqrt{5} + \sqrt{3})}{(\sqrt{5} - \sqrt{3}) (\sqrt{5} + \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{x (\sqrt{5} + \sqrt{3})}{{\sqrt{5}}^{2} + \sqrt{15} - \sqrt{15} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{x (\sqrt{5} + \sqrt{3})}{2}$