Question

In the following exercises, simplify each expression.

$\frac{4\left(-3+2\left(3-6\right)\right)}{3\left(11-3\left(2+3\right)\right)}$

Short answer

The simplified expression is$3$.

Step-by-step solution

Step 1. Given Information.

The given expression is$\frac{4\left(-3+2\left(3-6\right)\right)}{3\left(11-3\left(2+3\right)\right)}$.

Step 2. Simplify the numerator and the denominator separately. 

$$\begin{gathered} \frac{4\left(-3+2\left(3-6\right)\right)}{3\left(11-3\left(2+3\right)\right)} \\ =\frac{4\left(-3+2\left(-3\right)\right)}{3\left(11-3\left(5\right)\right)} \\ =\frac{4\left(-3+(-6)\right)}{3\left(11-15\right)} \\ =\frac{4\left(-3-6\right)}{3\left(-4\right)} \\ =\frac{4(-9)}{-12} \\ =\frac{-36}{-12} \\ =3 \end{gathered}$$

Step 3. Conclusion. 

The simplified form of the given expression is$3$.