Simplify -6/(8+ square root of 14)

$\frac{- 6}{8 + \sqrt{14}}$

Step 1

Move the negative in front of the fraction.

$- \frac{6}{8 + \sqrt{14}}$

Step 2

Multiply $\frac{6}{8 + \sqrt{14}}$ by $\frac{8 - \sqrt{14}}{8 - \sqrt{14}}$ .

$- (\frac{6}{8 + \sqrt{14}} \cdot \frac{8 - \sqrt{14}}{8 - \sqrt{14}})$

Step 3

Multiply $\frac{6}{8 + \sqrt{14}}$ by $\frac{8 - \sqrt{14}}{8 - \sqrt{14}}$ .

$- \frac{6 (8 - \sqrt{14})}{(8 + \sqrt{14}) (8 - \sqrt{14})}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{6 (8 - \sqrt{14})}{64 - 8 \sqrt{14} + \sqrt{14} \cdot 8 - {\sqrt{14}}^{2}}$

Step 5

Simplify.

$- \frac{6 (8 - \sqrt{14})}{50}$

Step 6

Cancel the common factor of $6$ and $50$ .

Factor $2$ out of $6 (8 - \sqrt{14})$ .

$- \frac{2 (3 (8 - \sqrt{14}))}{50}$

Cancel the common factors.

Factor $2$ out of $50$ .

$- \frac{2 (3 (8 - \sqrt{14}))}{2 (25)}$

Cancel the common factor.

$- \frac{2 (3 (8 - \sqrt{14}))}{2 \cdot 25}$

Rewrite the expression.

$- \frac{3 (8 - \sqrt{14})}{25}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 (8 - \sqrt{14})}{25}$

Decimal Form:

$- 0.51100111 \dots$