Algebra Examples

$\frac{\sqrt{11}}{\sqrt{5} - 3}$

Step 1

Multiply $\frac{\sqrt{11}}{\sqrt{5} - 3}$ by $\frac{\sqrt{5} + 3}{\sqrt{5} + 3}$ .

$\frac{\sqrt{11}}{\sqrt{5} - 3} \cdot \frac{\sqrt{5} + 3}{\sqrt{5} + 3}$

Step 2

Simplify terms.

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Step 2.1

Multiply $\frac{\sqrt{11}}{\sqrt{5} - 3}$ by $\frac{\sqrt{5} + 3}{\sqrt{5} + 3}$ .

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

Step 2.2

Expand the denominator using the FOIL method.

$\frac{\sqrt{11} (\sqrt{5} + 3)}{{\sqrt{5}}^{2} + \sqrt{5} \cdot 3 - 3 \sqrt{5} - 9}$

Step 2.3

Simplify.

$\frac{\sqrt{11} (\sqrt{5} + 3)}{- 4}$

Step 2.4

Apply the distributive property.

$\frac{\sqrt{11} \sqrt{5} + \sqrt{11} \cdot 3}{- 4}$

Step 2.5

Combine using the product rule for radicals.

$\frac{\sqrt{11 \cdot 5} + \sqrt{11} \cdot 3}{- 4}$

Step 2.6

Move $3$ to the left of $\sqrt{11}$ .

$\frac{\sqrt{11 \cdot 5} + 3 \cdot \sqrt{11}}{- 4}$

Step 3

Multiply $11$ by $5$ .

$\frac{\sqrt{55} + 3 \sqrt{11}}{- 4}$

Step 4

Move the negative in front of the fraction.

$- \frac{\sqrt{55} + 3 \sqrt{11}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{55} + 3 \sqrt{11}}{4}$

Decimal Form:

$- 4.34151821 \dots$