Simplify 7/(-10- square root of 17)

$\frac{7}{- 10 - \sqrt{17}}$

Step 1

Multiply $\frac{7}{- 10 - \sqrt{17}}$ by $\frac{- 10 + \sqrt{17}}{- 10 + \sqrt{17}}$ .

$\frac{7}{- 10 - \sqrt{17}} \cdot \frac{- 10 + \sqrt{17}}{- 10 + \sqrt{17}}$

Step 2

Multiply $\frac{7}{- 10 - \sqrt{17}}$ by $\frac{- 10 + \sqrt{17}}{- 10 + \sqrt{17}}$ .

$\frac{7 (- 10 + \sqrt{17})}{(- 10 - \sqrt{17}) (- 10 + \sqrt{17})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{7 (- 10 + \sqrt{17})}{100 - 10 \sqrt{17} + 10 \sqrt{17} - {\sqrt{17}}^{2}}$

Step 4

Simplify.

$\frac{7 (- 10 + \sqrt{17})}{83}$

Step 5

Rewrite $- 10$ as $- 1 (10)$ .

$\frac{7 (- 1 (10) + \sqrt{17})}{83}$

Step 6

Factor $- 1$ out of $\sqrt{17}$ .

$\frac{7 (- 1 (10) - 1 (- \sqrt{17}))}{83}$

Step 7

Factor $- 1$ out of $- 1 (10) - 1 (- \sqrt{17})$ .

$\frac{7 (- 1 (10 - \sqrt{17}))}{83}$

Step 8

Move the negative in front of the fraction.

$- \frac{7 (10 - \sqrt{17})}{83}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 (10 - \sqrt{17})}{83}$

Decimal Form:

$- 0.49564169 \dots$