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Asked: 2026-05-23T15:20:55+00:00

I had tried the code below in Mathematica 8: f[z_] := (5 + 1/(z-a))

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I had tried the code below in Mathematica 8:

f[z_] := (5 + 1/(z-a)) / ( 8 + 1/(z-a))

f[a]

and surprisingly I got following warnings:

Power::infy: Infinite expression 1/0 encountered. >>
Power::infy: Infinite expression 1/0 encountered. >>
Infinity::indet: Indeterminate expression 0 ComplexInfinity encountered. >

and the output is Indeterminate, which I think is not true because obviously it’s 1.

What’s weird is that when I changed the code to:

Simplify[(5 + 1/(z-a)) / ( 8 + 1/(z-a))] /. a -> z

I got the correct output 1. Why is that? And how should I deal with expressions involving ∞/∞ ?

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1 Answer

  1. Editorial Team

    Usually: 

    Limit[(5 + 1/(z - a))/(8 + 1/(z - a)), z -> a]
(*
-> 1
*)

    Edit

    You may also add a Direction option to take the limit coming from either side if necessary: 

    Limit[(5 + 1/(z - a))/(8 + 1/(z - a)), z -> a, Direction -> 1]

    or 

    Limit[(5 + 1/(z - a))/(8 + 1/(z - a)), z -> a, Direction -> -1]

    Edit 2

    The weird behavior of Simplify[ ] (allowing some mathematically indefinite expressions to evaluate) is well documented in the help:

    enter image description here

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