$\displaystyle \[\left | \frac{1}{x-1} \right |>\left | \frac{x+3}{2x+1} \right |\]$

Can anyone give a step by step method of solving this type of question please.

The solutions given are:

-2-sqrt(6)< x <-3

-3<= x < -2

-2+sqrt(6) < x < 1

1 < x < 2

Thank you in advance!