Question 733607
I assume you meant 2/(x+1) - 4/(x+2) = 3x/(x^2 + 3x+2) or {{{2/(x+1) - 4/(x+2) = 3x/(x^2 + 3x+2)}}}
Since {{{(x+1)(x+2)=x^3+3x+2}}} I would multiply both sides of the equation times that to get
{{{2(x+1)(x+2)/(x+1) - 4(x+1)(x+2)/(x+2) = 3x(x+1)(x+2)/(x^2 + 3x+2)}}}
That simplifies to
{{{2(x+2)-4(x+1)=3x}}}
Doing the indicated multiplications we get
{{{2x+4-4x-4=3x}}} which simplifies to
{{{2x-4x=3x}}} --> {{{2x-4x+4x-2x=3x+4x-2x}}} --> {{{0=5x}}} --> {{{highlight(x=0)}}}
There are no more solutions.
Verification:
substituting 0 for x we get
{{{2/1-4/2=0/2}}} or {{{2-2=0}}}
So {{{x=0}}} is a solution.