Algebra Examples

$\frac{1}{3 - \sqrt{11}}$

Step 1

Multiply $\frac{1}{3 - \sqrt{11}}$ by $\frac{3 + \sqrt{11}}{3 + \sqrt{11}}$ .

$\frac{1}{3 - \sqrt{11}} \cdot \frac{3 + \sqrt{11}}{3 + \sqrt{11}}$

Step 2

Multiply $\frac{1}{3 - \sqrt{11}}$ by $\frac{3 + \sqrt{11}}{3 + \sqrt{11}}$ .

$\frac{3 + \sqrt{11}}{(3 - \sqrt{11}) (3 + \sqrt{11})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{3 + \sqrt{11}}{9 + 3 \sqrt{11} - 3 \sqrt{11} - {\sqrt{11}}^{2}}$

Step 4

Simplify.

$\frac{3 + \sqrt{11}}{- 2}$

Step 5

Move the negative in front of the fraction.

$- \frac{3 + \sqrt{11}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 + \sqrt{11}}{2}$

Decimal Form:

$- 3.15831239 \dots$