Pre-Algebra Examples

$\frac{x}{\sqrt{15} - \sqrt{3}}$

Step 1

Multiply $\frac{x}{\sqrt{15} - \sqrt{3}}$ by $\frac{\sqrt{15} + \sqrt{3}}{\sqrt{15} + \sqrt{3}}$ .

$\frac{x}{\sqrt{15} - \sqrt{3}} \cdot \frac{\sqrt{15} + \sqrt{3}}{\sqrt{15} + \sqrt{3}}$

Step 2

Multiply $\frac{x}{\sqrt{15} - \sqrt{3}}$ by $\frac{\sqrt{15} + \sqrt{3}}{\sqrt{15} + \sqrt{3}}$ .

$\frac{x (\sqrt{15} + \sqrt{3})}{(\sqrt{15} - \sqrt{3}) (\sqrt{15} + \sqrt{3})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{x (\sqrt{15} + \sqrt{3})}{{\sqrt{15}}^{2} + \sqrt{45} - \sqrt{45} - {\sqrt{3}}^{2}}$

Step 4

Simplify.

$\frac{x (\sqrt{15} + \sqrt{3})}{12}$

Step 5

Apply the distributive property.

$\frac{x \sqrt{15} + x \sqrt{3}}{12}$

Step 6

Split the fraction $\frac{x \sqrt{15} + x \sqrt{3}}{12}$ into two fractions.

$\frac{x \sqrt{15}}{12} + \frac{x \sqrt{3}}{12}$