Simplify 2/(-2-3 square root of 2)

$\frac{2}{- 2 - 3 \sqrt{2}}$

Step 1

Multiply $\frac{2}{- 2 - 3 \sqrt{2}}$ by $\frac{- 2 + 3 \sqrt{2}}{- 2 + 3 \sqrt{2}}$ .

$\frac{2}{- 2 - 3 \sqrt{2}} \cdot \frac{- 2 + 3 \sqrt{2}}{- 2 + 3 \sqrt{2}}$

Step 2

Multiply $\frac{2}{- 2 - 3 \sqrt{2}}$ by $\frac{- 2 + 3 \sqrt{2}}{- 2 + 3 \sqrt{2}}$ .

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

Step 3

Expand the denominator using the FOIL method.

$\frac{2 (- 2 + 3 \sqrt{2})}{4 - 6 \sqrt{2} + 6 \sqrt{2} - 9 {\sqrt{2}}^{2}}$

Step 4

Simplify.

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

Step 5

Cancel the common factors.

Factor $2$ out of $- 14$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 2 + 3 \sqrt{2}}{- 7}$

Step 6

Move the negative in front of the fraction.

$- \frac{- 2 + 3 \sqrt{2}}{7}$

Step 7

Rewrite $- 2$ as $- 1 (2)$ .

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

Step 8

Factor $- 1$ out of $3 \sqrt{2}$ .

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

Step 9

Factor $- 1$ out of $- 1 (2) - (- 3 \sqrt{2})$ .

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

Step 10

Simplify the expression.

Move the negative in front of the fraction.

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

Multiply $- 1$ by $- 1$ .

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

Multiply $\frac{2 - 3 \sqrt{2}}{7}$ by $1$ .

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

Step 11

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.32037724 \dots$

Simplify 2/(-2-3 square root of 2)

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