Basic Math Examples

$\frac{a}{\sqrt{10} - \sqrt{7}}$

Step 1

Multiply $\frac{a}{\sqrt{10} - \sqrt{7}}$ by $\frac{\sqrt{10} + \sqrt{7}}{\sqrt{10} + \sqrt{7}}$ .

$\frac{a}{\sqrt{10} - \sqrt{7}} \cdot \frac{\sqrt{10} + \sqrt{7}}{\sqrt{10} + \sqrt{7}}$

Step 2

Multiply $\frac{a}{\sqrt{10} - \sqrt{7}}$ by $\frac{\sqrt{10} + \sqrt{7}}{\sqrt{10} + \sqrt{7}}$ .

$\frac{a (\sqrt{10} + \sqrt{7})}{(\sqrt{10} - \sqrt{7}) (\sqrt{10} + \sqrt{7})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{a (\sqrt{10} + \sqrt{7})}{{\sqrt{10}}^{2} + \sqrt{70} - \sqrt{70} - {\sqrt{7}}^{2}}$

Step 4

Simplify.

$\frac{a (\sqrt{10} + \sqrt{7})}{3}$