Answer
$(-1/2, 0) U (1/2, ∞)$
Work Step by Step
Values of x in which $f(x) > g(x)$
Given $f(x) = 4x$ and $g(x) = \frac {1}{x}$
$4x > \frac{1}{x-1}$
$4x - \frac {1}{x} > 0 $
$\frac {4x^2 - 1}{(x)} > 0$
$\frac {(2x-1)(2x+1)}{x} > 0$
Find the zeros of the expressions in the numerator AND the denominator
$x = -1/2, 1/2, 0$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -1/2) $\frac {(-)(-)}{(-)} = (-)$
(-1/2, 0) $\frac {(-)(+)}{(-)} = (+)$
(0, 1/2) $\frac {(-)(+)}{(+)} = (-)$
(1/2, ∞) $\frac {(+)(+)}{(+)} = (+)$
Thus the solution is $(-1/2, 0) U (1/2, ∞)$