Algebra Examples

$\frac{7}{\sqrt{6} + \sqrt{5}}$

Step 1

Multiply $\frac{7}{\sqrt{6} + \sqrt{5}}$ by $\frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} - \sqrt{5}}$ .

$\frac{7}{\sqrt{6} + \sqrt{5}} \cdot \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} - \sqrt{5}}$

Step 2

Multiply $\frac{7}{\sqrt{6} + \sqrt{5}}$ by $\frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} - \sqrt{5}}$ .

$\frac{7 (\sqrt{6} - \sqrt{5})}{(\sqrt{6} + \sqrt{5}) (\sqrt{6} - \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (\sqrt{6} - \sqrt{5})}{{\sqrt{6}}^{2} - \sqrt{30} + \sqrt{30} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{7 (\sqrt{6} - \sqrt{5})}{1}$

Step 5

Divide $7 (\sqrt{6} - \sqrt{5})$ by $1$ .

$7 (\sqrt{6} - \sqrt{5})$

Step 6

Apply the distributive property.

$7 \sqrt{6} + 7 (- \sqrt{5})$

Step 7

Multiply $- 1$ by $7$ .

$7 \sqrt{6} - 7 \sqrt{5}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{6} - 7 \sqrt{5}$

Decimal Form:

$1.49395235 \dots$