Basic Math Examples

$\frac{- 6 - \sqrt{- 12}}{48}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{- 6 - \sqrt{- 1 (12)}}{48}$

Step 1.2

Rewrite $\sqrt{- 1 (12)}$ as $\sqrt{- 1} \cdot \sqrt{12}$ .

$\frac{- 6 - (\sqrt{- 1} \cdot \sqrt{12})}{48}$

Step 1.3

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{- 6 - (i \cdot \sqrt{12})}{48}$

$\frac{- 6 - (i \cdot \sqrt{12})}{48}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 2.1.1

Factor $4$ out of $12$ .

$\frac{- 6 - i \cdot \sqrt{4 (3)}}{48}$

Step 2.1.2

Rewrite $4$ as $2^{2}$ .

$\frac{- 6 - i \cdot \sqrt{2^{2} \cdot 3}}{48}$

$\frac{- 6 - i \cdot \sqrt{2^{2} \cdot 3}}{48}$

Step 2.2

Pull terms out from under the radical.

$\frac{- 6 - i \cdot (2 \sqrt{3})}{48}$

Step 2.3

Multiply $2$ by $- 1$ .

$\frac{- 6 - 2 i \sqrt{3}}{48}$

$\frac{- 6 - 2 i \sqrt{3}}{48}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $- 6 - 2 i \sqrt{3}$ and $48$ .

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Step 3.1.1

Factor $2$ out of $- 6$ .

$\frac{2 (- 3) - 2 i \sqrt{3}}{48}$

Step 3.1.2

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

$\frac{2 (- 3) + 2 (- i \sqrt{3})}{48}$

Step 3.1.3

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

$\frac{2 (- 3 - i \sqrt{3})}{48}$

Step 3.1.4

Cancel the common factors.

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Step 3.1.4.1

Factor $2$ out of $48$ .

$\frac{2 (- 3 - i \sqrt{3})}{2 \cdot 24}$

Step 3.1.4.2

Cancel the common factor.

$\frac{2 (- 3 - i \sqrt{3})}{2 \cdot 24}$

Step 3.1.4.3

Rewrite the expression.

$\frac{- 3 - i \sqrt{3}}{24}$

$\frac{- 3 - i \sqrt{3}}{24}$

$\frac{- 3 - i \sqrt{3}}{24}$

Step 3.2

Rewrite $- 3$ as $- 1 (3)$ .

$\frac{- 1 (3) - i \sqrt{3}}{24}$

Step 3.3

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

$\frac{- 1 (3) - (i \sqrt{3})}{24}$

Step 3.4

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

$\frac{- 1 (3 + i \sqrt{3})}{24}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{3 + i \sqrt{3}}{24}$

$- \frac{3 + i \sqrt{3}}{24}$

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