(x+2)(x+1)-(x-3)(x+6)
=(x²+3x+2)-(x²+3x-18)
=x²+3x+2-x²-3x+18
=20>0
所以(x+2)(x+1)-(x-3)(x+6)>0
所以(x+2)(x+1)>(x-3)(x+6)