Simplify -7/(3 square root of 2-1)

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

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

Step 3

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

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

Step 4

Expand the denominator using the FOIL method.

$- \frac{7 (3 \sqrt{2} + 1)}{9 {\sqrt{2}}^{2} + 3 \sqrt{2} - 3 \sqrt{2} - 1}$

Step 5

Simplify.

$- \frac{7 (3 \sqrt{2} + 1)}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 (3 \sqrt{2} + 1)}{17}$

Decimal Form:

$- 2.15873440 \dots$