Finite Math Examples

$\frac{9}{\sqrt{11} + \sqrt{5}}$

Step 1

Multiply $\frac{9}{\sqrt{11} + \sqrt{5}}$ by $\frac{\sqrt{11} - \sqrt{5}}{\sqrt{11} - \sqrt{5}}$ .

$\frac{9}{\sqrt{11} + \sqrt{5}} \cdot \frac{\sqrt{11} - \sqrt{5}}{\sqrt{11} - \sqrt{5}}$

Step 2

Multiply $\frac{9}{\sqrt{11} + \sqrt{5}}$ by $\frac{\sqrt{11} - \sqrt{5}}{\sqrt{11} - \sqrt{5}}$ .

$\frac{9 (\sqrt{11} - \sqrt{5})}{(\sqrt{11} + \sqrt{5}) (\sqrt{11} - \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{9 (\sqrt{11} - \sqrt{5})}{{\sqrt{11}}^{2} - \sqrt{55} + \sqrt{55} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{9 (\sqrt{11} - \sqrt{5})}{6}$

Step 5

Cancel the common factor of $9$ and $6$ .

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Step 5.1

Factor $3$ out of $9 (\sqrt{11} - \sqrt{5})$ .

$\frac{3 (3 (\sqrt{11} - \sqrt{5}))}{6}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $6$ .

$\frac{3 (3 (\sqrt{11} - \sqrt{5}))}{3 (2)}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (3 (\sqrt{11} - \sqrt{5}))}{3 \cdot 2}$

Step 5.2.3

Rewrite the expression.

$\frac{3 (\sqrt{11} - \sqrt{5})}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3 (\sqrt{11} - \sqrt{5})}{2}$

Decimal Form:

$1.62083521 \dots$