What is the difference x +5/ x +2 - x + 1/x ^2 + 2x?

The difference will be given by:
(x +5)/ (x +2) - (x + 1)/(x ^2 + 2x)
=(x +5)/ (x +2) - (x + 1)/[x (x + 2)]
the LCM is x(x+2)
thus the difference will be:
[x(x+5)-(x+1)]/(x (x + 2))
=[x^2+5x-x-1]/[x(x+2)]
=(x^2-4x-1)/[x(x+2)]

Answer:(x^2-4x-1)/[x(x+2)]