Basic Math Examples

$\frac{1}{\sqrt{a} + \sqrt{a + b}}$

Step 1

Multiply $\frac{1}{\sqrt{a} + \sqrt{a + b}}$ by $\frac{\sqrt{a} - \sqrt{a + b}}{\sqrt{a} - \sqrt{a + b}}$ .

$\frac{1}{\sqrt{a} + \sqrt{a + b}} \cdot \frac{\sqrt{a} - \sqrt{a + b}}{\sqrt{a} - \sqrt{a + b}}$

Step 2

Multiply $\frac{1}{\sqrt{a} + \sqrt{a + b}}$ by $\frac{\sqrt{a} - \sqrt{a + b}}{\sqrt{a} - \sqrt{a + b}}$ .

$\frac{\sqrt{a} - \sqrt{a + b}}{(\sqrt{a} + \sqrt{a + b}) (\sqrt{a} - \sqrt{a + b})}$

Step 3

Expand the denominator using the FOIL method.

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

Step 4

Simplify.

$\frac{\sqrt{a} - \sqrt{a + b}}{- b}$

Step 5

Move the negative in front of the fraction.

$- \frac{\sqrt{a} - \sqrt{a + b}}{b}$