Question:
Divide:
$\frac{1}{4} x^{2}-\frac{1}{2} x-12$ by $\frac{1}{2} x-4$
Solution:
$\frac{\frac{1}{4} x^{2}-\frac{1}{2} x-12}{\frac{1}{2} x-4}$
$=\frac{\frac{1}{2} x\left(\frac{1}{2} x-4\right)+3\left(\frac{1}{2} x-4\right)}{\frac{1}{2} x-4}$
$=\frac{\left(\frac{1}{2} x-4\right)\left(\frac{1}{2} x+3\right)}{\left(\frac{1}{2} x-4\right)}$
$=\frac{1}{2} x+3$