i have an equation

x^2 + 5x +6

--------------

x+2

and get the graph of y=x shifted 3 units up, and when x = -2 there is a one point assymptote.

but when i simpify that equation i get x+3

and the graph is a y=x shifted 3 units up, and no point of assymptote.

so i know both equations are equal to each other, but what would be the correct graph of it since there are two different graphs...???

can someone explain all this....