Answer
$(-∞, 0)) U (1, ∞)$
Work Step by Step
Values of x in which $f(x) > g(x)$
Given $f(x) = x^2 + x$ and $g(x) = \frac {2}{x}$
$x^2 + x > \frac{2}{x}$
$x^2 + x - \frac {2}{x} > 0 $
$\frac {x^3 +x^2 - 2}{(x)} > 0$
$\frac {x^3 -x^2 + 2x^2- 2}{(x)} > 0$
$\frac {x^2(x-1) + 2(x^2- 1)}{(x)} > 0$
$\frac {(x-1) (x^2 + 2(x+1))}{(x)} > 0$
$\frac {(x-1) (x^2 + 2x+2)}{(x)} > 0$
Find the zeros of the expressions in the numerator AND the denominator
$x = 1, 0$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, 0) $\frac {(-)(+)}{(-)} = (+)$
(0, 1) $\frac {(-)(+)}{(+)} = (-)$
(1, ∞) $\frac {(+)(+)}{(+)} = (+)$
Thus the solution is $(-∞, 0)) U (1, ∞)$
