Question 907734
{{{(3x/(x^2+5x+6))=(5x/(x^2+2x-3))-(2/(x^2+x-2))}}}
Multiplying both sides of the equal sign times {{{(x+3)(x+2)(x-1)}}} ,
you get an equivalent equation, except that you may get some extraneous solution(s) that would make the LCD and some denominator equal to zero.
The equivalent equation and solution follow.
{{{3x(x-1)=5x(x+2)-2(x+3)}}}
{{{3x^2-3x=5x^2+10x-2x-6}}}
{{{3x^2-3x=5x^2+8x-6}}}
{{{2x^2+11x-6=0}}}
The polynomial on the left can be factored to get
{{{(2x-1)(x+6)=0}}}
So either {{{2x-1=0}}}--->{{{highlight(x=1/2)}}} ,
or {{{x+6=0}}}--->{{{highlight(x=-6)}}} .
Both answers are valid since they do not make any denominator equal to zero.