Hi aird,

I think you don't need to define a user-defined function for: 
   y=c/(t-t0)
because Origin has a built-in function Rational4 in Rational category:
   y=c+b/(x+a)
In the fitting process of NLFit, you can fix the value of c (of Rational4) to 0 
(by turning ON the "Fixed" check box in the Parameter tab, and double-click 
the value, and enter 0). 

By the way, for defining a user-defined function, maybe the following 
tutorials may be helpul:

(Video)
http://www.originlab.com/index.aspx?go=Products/Origin/DataAnalysis/CurveFitting/FittingFunctions&pid=1172

(Text)
http://wiki.originlab.com/~originla/howto/index.php?title=Tutorial:User_Defined_Fitting_Function_using_OC

As your Origin version is 8.0, it doesn't have more convenient 
"Fitting Function Builder" (available in 8.5, or later), and 
you need to skip the section in the (Text) tutorial.

Hope this helps.

--Hideo Fujii
OriginLab