Question 818521
Do as {{{x/(x+1)-6x>0}}}, then multiply left and right by x+1.  Realize x+1 may be either positive, zero ; or less than zero so:


If {{{x+1<0}}} then {{{x-6x(x+1)<0}}};


If {{{x+1>=0}}} then {{{x-6x(x+1)>0}}};


So work with those both.  Also realize, {{{x<>-1}}}.  Also, before solving both inequalities, you do not yet know if they form an intersection or a union.  
The x at -1 is a critical point, and when you solve each of the two main inequalities each of them is also a critical point, so the critical points help form your intervals on x.    You check any value in every interval to see if the original given inequality is satisfied or not satisfied.


Can you continue with this guidance as described?