Simplify 7/(-2+ square root of 13)

$\frac{7}{- 2 + \sqrt{13}}$

Step 1

Multiply $\frac{7}{- 2 + \sqrt{13}}$ by $\frac{- 2 - \sqrt{13}}{- 2 - \sqrt{13}}$ .

$\frac{7}{- 2 + \sqrt{13}} \cdot \frac{- 2 - \sqrt{13}}{- 2 - \sqrt{13}}$

Step 2

Multiply $\frac{7}{- 2 + \sqrt{13}}$ by $\frac{- 2 - \sqrt{13}}{- 2 - \sqrt{13}}$ .

$\frac{7 (- 2 - \sqrt{13})}{(- 2 + \sqrt{13}) (- 2 - \sqrt{13})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (- 2 - \sqrt{13})}{4 + 2 \sqrt{13} + \sqrt{13} \cdot - 2 - {\sqrt{13}}^{2}}$

Step 4

Simplify.

$\frac{7 (- 2 - \sqrt{13})}{- 9}$

Step 5

Move the negative in front of the fraction.

$- \frac{7 (- 2 - \sqrt{13})}{9}$

Step 6

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

$- \frac{7 (- 1 (2) - \sqrt{13})}{9}$

Step 7

Factor $- 1$ out of $- \sqrt{13}$ .

$- \frac{7 (- 1 (2) - (\sqrt{13}))}{9}$

Step 8

Factor $- 1$ out of $- 1 (2) - (\sqrt{13})$ .

$- \frac{7 (- 1 (2 + \sqrt{13}))}{9}$

Step 9

Simplify the expression.

Move the negative in front of the fraction.

$- - \frac{7 (2 + \sqrt{13})}{9}$

Multiply $- 1$ by $- 1$ .

$1 \frac{7 (2 + \sqrt{13})}{9}$

Multiply $\frac{7 (2 + \sqrt{13})}{9}$ by $1$ .

$\frac{7 (2 + \sqrt{13})}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{7 (2 + \sqrt{13})}{9}$

Decimal Form:

$4.35987321 \dots$