Question

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

Answer 1

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

$\frac{1}{4}{x}^2-\frac{1}{2}x-12=\frac{1}{4}(x^2-2x-48)$

$\frac{1}{4}\{x^2-8x+6x-48\}\{\begin{array}{cc}\because -48=-8\times 6& \\ -2=-8+6& \end{array}$

$=\frac{1}{4}\left\{x\right(x-8)+6(x-8\left)\right\}$

$=\frac{1}{4}(x-8)(x+6)$

$\therefore \frac{\frac{1}{4}{x}^2-\frac{1}{2}x-12}{\frac{1}{2}x-4}=\frac{\frac{1}{4}(x-8)(x+6)}{\frac{1}{2}(x-8)}$

$=\frac{1}{4}\times \frac{2}{1}(x+6)$

$=\frac{1}{2}(x+6)=\frac{1}{2}x+3$