Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

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

Step 5

Simplify the expression.

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Step 5.1

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

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

Step 5.2

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

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

Step 6

Apply the distributive property.

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