Question 950736
Break up the number line based on the critical values of your equation (that is, when it goes to zero or becomes undefined).
In this case,{{{x=-3}}}, {{{x=4}}}, and {{{x=6}}}.
This breaks the number line into 4 regions.
Region 1: {{{x<-3}}}
Region 2:{{{-3<x<4}}}
Region 3:{{{4<x<6}}}
Region 4:{{{x>6}}}
Now choose a point in each region (not an endpoint) and test the inequality.
If it's true, that region is part of the solution region.
If it's false, that region is not part of the solution region.
Region 1: {{{x=-4}}}
{{{((-4+3)(-4-6))/(-4-4)<0}}}
{{{((-1)(-10))/(-8)<0}}}
{{{-10/8<0}}}
True, part of the solution.
Region 2: {{{x=0}}}
{{{((0+3)(0-6))/(0-4)<0}}}
{{{(-18)/(-4)<0}}}
{{{9/2<0}}}
False, not part of the solution.
Region 3: {{{x=5}}}
{{{((5+3)(5-6))/(5-4)<0}}}
{{{((8)(-1))/(1)<0}}}
{{{-8<0}}}
True, part of the solution.
Region 4: {{{x=7}}}
{{{((7+3)(7-6))/(7-4)<0}}}
{{{((10)(1))/(3)<0}}}
{{{10/3<0}}}
False, not part of the solution.
So then putting it all together,
Solution Region:({{{-infinity}}},{{{-3}}})U({{{4}}},{{{6}}})
{{{graph(300,300,-10,10,-10,10,((x+3)(x-6))/(x-4))}}}