Question 907734
{{{(3x/(x^2+5x+6))=(5x/(x^2+2x-3))-(2/(x^2+x-2))}}}


{{{(3x/((x+2)(x+3)))=(5x/((x-1)(x+3)))-(2/((x+2)(x-1)))}}}


LCD is {{{(x+2)(x+3)(x-1)}}}, same as what you found.



{{{(x+2)(x+3)(x-1)(3x/((x+2)(x+3)))=(x+2)(x+3)(x-1)(5x/((x-1)(x+3)))-(x+2)(x+3)(x-1)(2/((x+2)(x-1)))}}}


{{{(x-1)(3x)=(x+2)(5x)-((x+3)2)}}}


{{{3x^2-3x=5x^2+10x-(2x+6)}}}
{{{3x^2-3x=5x^2+10x-2x-6}}}
{{{-2x^2-3x-10x+2x+6=0}}}
{{{-2x^2-11x+6=0}}}
{{{highlight_green(2x^2+11x-6=0)}}} after multiplying left and right by {{{-1}}}.
FACTORABLE:
{{{highlight_green((2x-1)(x+6)=0)}}}
{{{highlight(x=1/2)}}}  OR  {{{highlight(x=-6)}}}