Couldn't get the LaTex to work, so here it is:
(3+1/x) / (3-1/x)
$\displaystyle \displaystyle \frac{3 + \frac{1}{x}}{3 - \frac{1}{x}} = \frac{\frac{3x + 1}{x}}{\frac{3x - 1}{x}}$
$\displaystyle \displaystyle = \frac{3x + 1}{3x - 1}$
$\displaystyle \displaystyle = \frac{3x - 1 + 2}{3x - 1}$
$\displaystyle \displaystyle = 1 + \frac{2}{3x - 1}$.
Pick whichever form you think is "simplest".