Answer
We can simplify $12\left( \frac{x+2}{4}-\frac{x-1}{3} \right)$ to $10-x$.
Work Step by Step
Consider the expression, $12\left( \frac{x+2}{4}-\frac{x-1}{3} \right)$
Apply the distributive property: $a\left( b+c \right)=ab+ac$
Therefore,
$\begin{align}
& 12\left( \frac{x+2}{4}-\frac{x-1}{3} \right)=\frac{12\left( x+2 \right)}{4}-\frac{12\left( x-1 \right)}{3} \\
& =3\left( x+2 \right)-4\left( x-1 \right)
\end{align}$
Apply the distributive property: $a\left( b+c \right)=ab+ac$
Therefore,
$\begin{align}
& 12\left( \frac{x+2}{4}-\frac{x-1}{3} \right)=3\left( x+2 \right)-4\left( x-1 \right) \\
& =3x+6-4x+4 \\
& =10-x
\end{align}$
Therefore, multiply and simplify the expression
$12\left( \frac{x+2}{4}-\frac{x-1}{3} \right)$ is $10-x$.
