Basic Math Examples

$\frac{- 8 + 6 \sqrt{2}}{10}$

Step 1

Cancel the common factor of $- 8 + 6 \sqrt{2}$ and $10$ .

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Step 1.1

Factor $2$ out of $- 8$ .

$\frac{2 (- 4) + 6 \sqrt{2}}{10}$

Step 1.2

Factor $2$ out of $6 \sqrt{2}$ .

$\frac{2 (- 4) + 2 (3 \sqrt{2})}{10}$

Step 1.3

Factor $2$ out of $2 (- 4) + 2 (3 \sqrt{2})$ .

$\frac{2 (- 4 + 3 \sqrt{2})}{10}$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $10$ .

$\frac{2 (- 4 + 3 \sqrt{2})}{2 \cdot 5}$

Step 1.4.2

Cancel the common factor.

$\frac{2 (- 4 + 3 \sqrt{2})}{2 \cdot 5}$

Step 1.4.3

Rewrite the expression.

$\frac{- 4 + 3 \sqrt{2}}{5}$

$\frac{- 4 + 3 \sqrt{2}}{5}$

$\frac{- 4 + 3 \sqrt{2}}{5}$

Step 2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + 3 \sqrt{2}}{5}$

Step 3

Factor $- 1$ out of $3 \sqrt{2}$ .

$\frac{- 1 (4) - (- 3 \sqrt{2})}{5}$

Step 4

Factor $- 1$ out of $- 1 (4) - (- 3 \sqrt{2})$ .

$\frac{- 1 (4 - 3 \sqrt{2})}{5}$

Step 5

Move the negative in front of the fraction.

$- \frac{4 - 3 \sqrt{2}}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{4 - 3 \sqrt{2}}{5}$

Decimal Form:

$0.04852813 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$