Question

Divide:
$\frac{1}{4}{x}^2-\frac{1}{2}x-12\mathrm{by}\frac{1}{2}x-4$

Answer 1

$$\begin{gathered} \frac{{\displaystyle \frac{\mathit{1}}{\mathit{4}}}{x}^{\mathit{2}}\mathit{-}{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{-}\mathit{12}}{{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{-}\mathit{4}} \\ \mathit{=}\frac{{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{(}{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{-}\mathit{4}\mathit{)}\mathit{+}\mathit{3}\mathit{(}{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{-}\mathit{4}\mathit{)}}{{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{-}\mathit{4}} \\ \mathit{=}\frac{\mathit{(}{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{-}\mathit{4}\mathit{)}\mathit{(}{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{+}\mathit{3}\mathit{)}}{\mathit{(}{\displaystyle \frac{\mathit{1}}{\mathit{2}}}x\mathit{-}\mathit{4}\mathit{)}} \\ \mathit{=}\frac{\mathit{1}}{\mathit{2}}x\mathit{+}\mathit{3} \end{gathered}$$