(x+1+1)/(x+1)+(x+2+1)/(x+2)>=(x+1)/x+(x+3+1)/(x+3)
1+1/(x+1)+1+1/(x+2)>=1+1/x+1+1/(x+3)
1/(x+1)+1/(x+2)>=1/x+1/(x+3)
1/(x+2)-1/(x+3)>=1/x-1/(x+1)
1/(x^2+5x+6)-1/(x^2+x)>=0
(-4x-6)/(x+2)(x+3)x(x+1)>=0
(2x+3)(x+2)(x+3)x(x+1)