# Equations and graphs problem

• October 2nd 2009, 03:49 PM
Sneaky
Equations and graphs problem
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...???(Thinking)
can someone explain all this....
• October 2nd 2009, 03:57 PM
Matt Westwood
Subtle.

The functions (not "equations") are not technically equal to each other. The first one does not exist at $x = -2$ because $0/0$ is undefined.

If you get onto calculus you'll learn about "limits" and how the "limit" of the first function when x "tends towards" -2 is equal to 1. But the very fact of there being a zero on the bottom at one point means that, as it stands, the functions are indeed not the same.