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

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

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

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

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

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

Expand the denominator using the FOIL method.

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

Simplify.

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

Simplify the expression.

Move the negative one from the denominator of $\frac{\sqrt{x} + \sqrt{x + 2}}{- 1}$ .

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

Rewrite $- 1 \cdot (\sqrt{x} + \sqrt{x + 2})$ as $- (\sqrt{x} + \sqrt{x + 2})$ .

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

Apply the distributive property.

$- \sqrt{x} - \sqrt{x + 2}$