Limits and Rational Functions: What Rule Must Be Followed When Evaluating at 0?

[Ry122]

what rule are you supposed to follow when you evaluate a rational function at 0? eg in this problem if you evaluate at s=0 for the one under "result" it will be different from the value obtained for the one under "alternate forms" http://www.wolframalpha.com/input/?i=(B/(m*(s^2)+k))/(1+(r*s^2+t*s)/(k*s+m*s^3))

What do I have to do to keep things consistent?

 

[Pzi]

what rule are you supposed to follow when you evaluate a rational function at 0? eg in this problem if you evaluate at s=0 for the one under "result" it will be different from the value obtained for the one under "alternate forms" http://www.wolframalpha.com/input/?i=(B/(m*(s^2)+k))/(1+(r*s^2+t*s)/(k*s+m*s^3))

What do I have to do to keep things consistent?

What exactly do you mean by "evaluation"?
At s=0 your initial input involves division by zero...
Well if you calculate a limit then everything is consistent.

 

[micromass]

This is the danger of programs like wolfram alpha. They're very good, but you got to be able to interpret the solution.

In this case, the "Input" and the "Alternate Form" are not equal. Indeed, the problem is that you can define by 0. In the "Input", if you put s=0, then you define by 0, so the "Input" is not defined at s=0.
But the "Alternate form" is defined at s=0 (whenever k+t is nonzero).

So the two forms are not equal since one is defined at s=0 and the other is not.

However, the limit of the "Input" as s goes to 0 does exist and does equal the "Alternate Form". So in the limit, the expressions are equal. But as rational forms, the expressions are not equal.