3/x+x/(x+2)=(-2)/(x+2)
:.(3(x+2)+(x)(x)=-2(x))/(x(x+2))
multiply L.H.S AND R.H.S. by color(purple)( x(x+2)
:.3x+6+x^2=-2x
:.3x+2x+x^2=-6
:.5x+x^2=-6
:.x^2+5x+6=0
:.(x+3)(x+2)=0
:.x+3=0 or x+2=0
:.color(purple)(x=-3 or color(purple)(x=-2
substitute color(purple)(x=-3
:.3/color(purple)(-3)+color(purple)(-3)/(color(purple)(-3)+2)=(-2)/(color(purple)(-3)+2)
:.-1+(-3)/-1=(-2)/(-1)
:.-1+3=2
:.2=2
substitute color(purple)(x=-2
:.3/color(purple)(-2)+color(purple)(-2)/(color(purple)(-2)+2)=(-2)/(color(purple)(-2)+2)
:.-1.5+(-2)/0=(-2)/0
extraneous solution, so x can't be -2