Simplify x/( square root of 5- square root of 2)

$\frac{x}{\sqrt{5} - \sqrt{2}}$

Step 1

Multiply $\frac{x}{\sqrt{5} - \sqrt{2}}$ by $\frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$ .

$\frac{x}{\sqrt{5} - \sqrt{2}} \cdot \frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$

Step 2

Multiply $\frac{x}{\sqrt{5} - \sqrt{2}}$ by $\frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{x (\sqrt{5} + \sqrt{2})}{{\sqrt{5}}^{2} + \sqrt{10} - \sqrt{10} - {\sqrt{2}}^{2}}$

Step 4

Simplify.

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