Evaluate (-4+12÷(-3))/(10+3(-2))

$\frac{- 4 + 12 \div (- 3)}{10 + 3 (- 2)}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of $12$ and $- 3$ .

Factor $3$ out of $12$ .

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

Move the negative one from the denominator of $\frac{4}{- 1}$ .

$\frac{- 4 - 1 \cdot 4}{10 + 3 (- 2)}$

Cancel the common factor of $- 4 - 1 \cdot 4$ and $10 + 3 (- 2)$ .

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

$\frac{- 1 (4) - 1 \cdot 4}{10 + 3 (- 2)}$

Factor $- 1$ out of $- 1 \cdot 4$ .

$\frac{- 1 (4) - 1 (4)}{10 + 3 (- 2)}$

Factor $- 1$ out of $- 1 (4) - 1 (4)$ .

$\frac{- 1 (4 + 4)}{10 + 3 (- 2)}$

Reorder terms.

$\frac{- 1 (4 + 4)}{10 - 2 \cdot 3}$

Factor $2$ out of $- 1 (4 + 4)$ .

$\frac{2 (- 1 (2 + 2))}{10 - 2 \cdot 3}$

Cancel the common factors.

Factor $2$ out of $10$ .

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

Factor $2$ out of $- 2 \cdot 3$ .

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

Factor $2$ out of $2 (5) + 2 (- 1 \cdot 3)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Add $2$ and $2$ .

$\frac{- 1 \cdot 4}{5 - 1 \cdot 3}$

Step 2

Simplify the denominator.

Multiply $- 1$ by $3$ .

$\frac{- 1 \cdot 4}{5 - 3}$

Subtract $3$ from $5$ .

$\frac{- 1 \cdot 4}{2}$

Step 3

Simplify the expression.

Multiply $- 1$ by $4$ .

$\frac{- 4}{2}$

Divide $- 4$ by $2$ .

$- 2$