Basic Math Examples

$\frac{- 4}{6} + \frac{2 \sqrt{13}}{6}$

Step 1

Combine the numerators over the common denominator.

$\frac{- 4 + 2 \sqrt{13}}{6}$

Step 2

Cancel the common factor of $- 4 + 2 \sqrt{13}$ and $6$ .

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Step 2.1

Factor $2$ out of $- 4$ .

$\frac{2 \cdot - 2 + 2 \sqrt{13}}{6}$

Step 2.2

Factor $2$ out of $2 \sqrt{13}$ .

$\frac{2 \cdot - 2 + 2 (\sqrt{13})}{6}$

Step 2.3

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

$\frac{2 \cdot (- 2 + \sqrt{13})}{6}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $2$ out of $6$ .

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

Step 2.4.2

Cancel the common factor.

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

Step 2.4.3

Rewrite the expression.

$\frac{- 2 + \sqrt{13}}{3}$

Step 3

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

$\frac{- 1 (2) + \sqrt{13}}{3}$

Step 4

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

$\frac{- 1 (2) - 1 (- \sqrt{13})}{3}$

Step 5

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

$\frac{- 1 (2 - \sqrt{13})}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{2 - \sqrt{13}}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{2 - \sqrt{13}}{3}$

Decimal Form:

$0.53518375 \dots$