Basic Math Examples

$\frac{- 2 (13 - \sqrt{9} + 2)}{14 - 4 \div 2}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $4$ and $2$ .

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Step 1.1.1

Factor $2$ out of $4$ .

$\frac{- 2 (13 - \sqrt{9} + 2)}{14 - 2 \cdot 2 \div 2}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2$ .

$\frac{- 2 (13 - \sqrt{9} + 2)}{14 - 2 \cdot 2 \div 2 (1)}$

Step 1.1.2.2

Cancel the common factor.

$\frac{- 2 (13 - \sqrt{9} + 2)}{14 - 2 \cdot 2 \div 2 \cdot 1}$

Step 1.1.2.3

Rewrite the expression.

$\frac{- 2 (13 - \sqrt{9} + 2)}{14 - \frac{2}{1}}$

Step 1.1.2.4

Divide $2$ by $1$ .

$\frac{- 2 (13 - \sqrt{9} + 2)}{14 - 1 \cdot 2}$

Step 1.2

Cancel the common factor of $- 2$ and $14 - 1 \cdot 2$ .

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Step 1.2.1

Rewrite $14$ as $- 1 (- 14)$ .

$\frac{- 2 (13 - \sqrt{9} + 2)}{- 1 (- 14) - 1 \cdot 2}$

Step 1.2.2

Factor $- 1$ out of $- 1 \cdot 2$ .

$\frac{- 2 (13 - \sqrt{9} + 2)}{- 1 (- 14) - 1 (2)}$

Step 1.2.3

Factor $- 1$ out of $- 1 (- 14) - 1 (2)$ .

$\frac{- 2 (13 - \sqrt{9} + 2)}{- 1 (- 14 + 2)}$

Step 1.2.4

Factor $2$ out of $- 2 (13 - \sqrt{9} + 2)$ .

$\frac{2 (- (13 - \sqrt{9} + 2))}{- 1 (- 14 + 2)}$

Step 1.2.5

Cancel the common factors.

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Step 1.2.5.1

Factor $2$ out of $- 1 (- 14 + 2)$ .

$\frac{2 (- (13 - \sqrt{9} + 2))}{2 (- 1 (- 7 + 1))}$

Step 1.2.5.2

Cancel the common factor.

$\frac{2 (- (13 - \sqrt{9} + 2))}{2 (- 1 (- 7 + 1))}$

Step 1.2.5.3

Rewrite the expression.

$\frac{- (13 - \sqrt{9} + 2)}{- 1 (- 7 + 1)}$

Step 1.3

Dividing two negative values results in a positive value.

$\frac{13 - \sqrt{9} + 2}{- 7 + 1}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

$\frac{13 - \sqrt{3^{2}} + 2}{- 7 + 1}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$\frac{13 - 1 \cdot 3 + 2}{- 7 + 1}$

Step 2.3

Multiply $- 1$ by $3$ .

$\frac{13 - 3 + 2}{- 7 + 1}$

Step 2.4

Subtract $3$ from $13$ .

$\frac{10 + 2}{- 7 + 1}$

Step 2.5

Add $10$ and $2$ .

$\frac{12}{- 7 + 1}$

Step 3

Simplify the expression.

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Step 3.1

Add $- 7$ and $1$ .

$\frac{12}{- 6}$

Step 3.2

Divide $12$ by $- 6$ .

$- 2$