Basic Math Examples

$\frac{8}{- 7 - \sqrt{5}}$

Step 1

Multiply $\frac{8}{- 7 - \sqrt{5}}$ by $\frac{- 7 + \sqrt{5}}{- 7 + \sqrt{5}}$ .

$\frac{8}{- 7 - \sqrt{5}} \cdot \frac{- 7 + \sqrt{5}}{- 7 + \sqrt{5}}$

Step 2

Multiply $\frac{8}{- 7 - \sqrt{5}}$ by $\frac{- 7 + \sqrt{5}}{- 7 + \sqrt{5}}$ .

$\frac{8 (- 7 + \sqrt{5})}{(- 7 - \sqrt{5}) (- 7 + \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{8 (- 7 + \sqrt{5})}{49 - 7 \sqrt{5} + 7 \sqrt{5} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{8 (- 7 + \sqrt{5})}{44}$

Step 5

Cancel the common factor of $8$ and $44$ .

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Step 5.1

Factor $4$ out of $8 (- 7 + \sqrt{5})$ .

$\frac{4 (2 (- 7 + \sqrt{5}))}{44}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $4$ out of $44$ .

$\frac{4 (2 (- 7 + \sqrt{5}))}{4 (11)}$

Step 5.2.2

Cancel the common factor.

$\frac{4 (2 (- 7 + \sqrt{5}))}{4 \cdot 11}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (- 7 + \sqrt{5})}{11}$

Step 6

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{2 (- 1 (7) + \sqrt{5})}{11}$

Step 7

Factor $- 1$ out of $\sqrt{5}$ .

$\frac{2 (- 1 (7) - 1 (- \sqrt{5}))}{11}$

Step 8

Factor $- 1$ out of $- 1 (7) - 1 (- \sqrt{5})$ .

$\frac{2 (- 1 (7 - \sqrt{5}))}{11}$

Step 9

Move the negative in front of the fraction.

$- \frac{2 (7 - \sqrt{5})}{11}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 (7 - \sqrt{5})}{11}$

Decimal Form:

$- 0.86616945 \dots$