Basic Math Examples

$\frac{- 26}{\sqrt{3} - 4}$

Step 1

Move the negative in front of the fraction.

$- \frac{26}{\sqrt{3} - 4}$

Step 2

Multiply $\frac{26}{\sqrt{3} - 4}$ by $\frac{\sqrt{3} + 4}{\sqrt{3} + 4}$ .

$- (\frac{26}{\sqrt{3} - 4} \cdot \frac{\sqrt{3} + 4}{\sqrt{3} + 4})$

Step 3

Multiply $\frac{26}{\sqrt{3} - 4}$ by $\frac{\sqrt{3} + 4}{\sqrt{3} + 4}$ .

$- \frac{26 (\sqrt{3} + 4)}{(\sqrt{3} - 4) (\sqrt{3} + 4)}$

Step 4

Expand the denominator using the FOIL method.

$- \frac{26 (\sqrt{3} + 4)}{{\sqrt{3}}^{2} + \sqrt{3} \cdot 4 - 4 \sqrt{3} - 16}$

Step 5

Simplify.

$- \frac{26 (\sqrt{3} + 4)}{- 13}$

Step 6

Cancel the common factor of $26$ and $- 13$ .

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Step 6.1

Factor $13$ out of $26 (\sqrt{3} + 4)$ .

$- \frac{13 (2 (\sqrt{3} + 4))}{- 13}$

Step 6.2

Move the negative one from the denominator of $\frac{2 (\sqrt{3} + 4)}{- 1}$ .

$- (- 1 \cdot (2 (\sqrt{3} + 4)))$

Step 7

Rewrite $- 1 \cdot (2 (\sqrt{3} + 4))$ as $- (2 (\sqrt{3} + 4))$ .

$- - (2 (\sqrt{3} + 4))$

Step 8

Apply the distributive property.

$- - (2 \sqrt{3} + 2 \cdot 4)$

Step 9

Multiply $2$ by $4$ .

$- - (2 \sqrt{3} + 8)$

Step 10

Apply the distributive property.

$- (- (2 \sqrt{3}) - 1 \cdot 8)$

Step 11

Multiply.

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Step 11.1

Multiply $2$ by $- 1$ .

$- (- 2 \sqrt{3} - 1 \cdot 8)$

Step 11.2

Multiply $- 1$ by $8$ .

$- (- 2 \sqrt{3} - 8)$

Step 12

Apply the distributive property.

$- (- 2 \sqrt{3}) - - 8$

Step 13

Multiply.

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Step 13.1

Multiply $- 2$ by $- 1$ .

$2 \sqrt{3} - - 8$

Step 13.2

Multiply $- 1$ by $- 8$ .

$2 \sqrt{3} + 8$

Step 14

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3} + 8$

Decimal Form:

$11.46410161 \dots$