(In reply to
re: Solution by Steven Lord)
I got sloppy. I first started working with x=10^2017 and had a thought if I added 1 to x then the fractions A and B would be a bit simpler. But I never double checked if I could just tweak the expressions and have things work correctly.
So trying again, let x = 10^2017. Then A=(200x+2)/(x^2+4x+6) and B=(200x+1)/(x^2+2x+3).
A-B = [-399x^2-600x]/[(x^2+4x+6)*(x^2+2x+5)]. This is obviously negative when x=10^2017, therefore B is greater.
re(2): Solution - trying again
