Basic Math Examples

$\frac{6}{\sqrt{7} + 2}$

Step 1

Multiply $\frac{6}{\sqrt{7} + 2}$ by $\frac{\sqrt{7} - 2}{\sqrt{7} - 2}$ .

$\frac{6}{\sqrt{7} + 2} \cdot \frac{\sqrt{7} - 2}{\sqrt{7} - 2}$

Step 2

Multiply $\frac{6}{\sqrt{7} + 2}$ by $\frac{\sqrt{7} - 2}{\sqrt{7} - 2}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{6 (\sqrt{7} - 2)}{{\sqrt{7}}^{2} + \sqrt{7} \cdot - 2 + 2 \sqrt{7} - 4}$

Step 4

Simplify.

$\frac{6 (\sqrt{7} - 2)}{3}$

Step 5

Cancel the common factor of $6$ and $3$ .

Tap for more steps...

Step 5.1

Factor $3$ out of $6 (\sqrt{7} - 2)$ .

$\frac{3 (2 (\sqrt{7} - 2))}{3}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 (\sqrt{7} - 2))}{3 (1)}$

Step 5.2.2

Cancel the common factor.

$\frac{3 (2 (\sqrt{7} - 2))}{3 \cdot 1}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (\sqrt{7} - 2)}{1}$

Step 5.2.4

Divide $2 (\sqrt{7} - 2)$ by $1$ .

$2 (\sqrt{7} - 2)$

Step 6

Apply the distributive property.

$2 \sqrt{7} + 2 \cdot - 2$

Step 7

Multiply $2$ by $- 2$ .

$2 \sqrt{7} - 4$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{7} - 4$

Decimal Form:

$1.29150262 \dots$