Question
Divide $\Big(\frac{1}{4}\text{x}^2-\frac{1}{2}\text{x}-12\Big)$ by $\Big(\frac{1}{2}\text{x}-4\Big)$
✓
Answer
$\frac{\frac{1}{4}\text{x}^2-\frac{1}{2}\text{x}-12}{\frac{1}{2}\text{x}-4}$
$=\frac{\frac{1}{2}\text{x}\Big(\frac{1}{2}\text{x}-4\Big)+3}{\frac{1}{2}\text{x}-4}$
$=\frac{\Big(\frac{1}{2}\text{x}+3\Big)\Big(\frac{1}{2}\text{x}-4\Big)}{\frac{1}{2}\text{x}-4}=\Big(\frac{1}{2}\text{x}+3\Big)$
$=\frac{\frac{1}{2}\text{x}\Big(\frac{1}{2}\text{x}-4\Big)+3}{\frac{1}{2}\text{x}-4}$
$=\frac{\Big(\frac{1}{2}\text{x}+3\Big)\Big(\frac{1}{2}\text{x}-4\Big)}{\frac{1}{2}\text{x}-4}=\Big(\frac{1}{2}\text{x}+3\Big)$
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