Precalculus (6th Edition) Blitzer

We can simplify $12\left( \frac{x+2}{4}-\frac{x-1}{3} \right)$ to $10-x$.
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 $10-x$.