Question 728270
{{{6/(x+4) > 6/(x-1)}}}, divide both sides by 6,
{{{1/(x+4)>1/(x-1)}}}
{{{1/(x+4)-1/(x-1)>0}}}
{{{((x-1)-(x+4))/((x+4)(x-1))>0}}}
{{{(-5)/((x+4)(x-1))>0}}}


One of the binomials of the denominator must be positive while the other is negative.  The critical points to test separating the intervals are at x=-4 and x=1.  Pick any value for x in each of these three intervals and test:


(-infinity, -4)
(-4, +1)
(+1, infinity)


The numerator is negative.  You must choose the intervals which make the entire denominator itself be negative.