Check your factorising, there's a -x^3 term on top but after the factorisation it's +ve.
4x^2 - x^3 - 4x
------------------- is > or = to 0
4x^2 - 1
i factored it to
x(x-2)(x-2)
------------- is > or = to 0
(2x-1)(2x+1)
i think
Solving Inequalities: An Overview
this is how to do it, but i can't figure out everything they're doing or how to apply it
thx