Question

How to simply ((4/x)-2)/((1/x)+3)

Answer 1

$\cfrac{~~ \frac{4}{x}-2~~}{\frac{1}{x}+3}\implies \cfrac{~~ \frac{4-2x}{\underset{\textit{using this LCD}}{x}}~~}{\frac{1 + 3x}{\underset{\textit{using this LCD}}{x}}}\implies \cfrac{4-2x}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1+3x}\implies \cfrac{2(2-x)}{1+3x}$