Simplify (-2(13- square root of 9+2))/(14-4÷2)

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

Reduce the expression by cancelling the common factors.

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

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Factor $2$ out of $4$ .

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

Cancel the common factors.

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Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2$ by $1$ .

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

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

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

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

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

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Dividing two negative values results in a positive value.

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

Simplify the numerator.

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

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

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

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

Multiply $- 1$ by $3$ .

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

Subtract $3$ from $13$ .

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

Add $10$ and $2$ .

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

Simplify the expression.

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Add $- 7$ and $1$ .

$\frac{12}{- 6}$

Divide $12$ by $- 6$ .

$- 2$

Simplify (-2(13- square root of 9+2))/(14-4÷2)

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