How do you inverse Laplace (s-9)/(s-5) ?

Question

How do you inverse Laplace (s-9)/(s-5)    ?

amistre64 · Answer

split the fraction maybe?

amistre64 · Answer

or .... split the top into s-5-4 then split the fraction

chrisplusian · Answer

I tried spliting the top but when I get s by itself I am stuck and don't know where to go from there..... if I split it to s-5-4 that would cancel the first fraction to just 1 and was not sure if it is ok to eliminate the variable that way?

amistre64 · Answer

youre allowed to do math ....

amistre64 · Answer

$$\frac{s-9}{s-5}~,~D:=\{s\in R|s\ne5\}$$
$$1-\frac{4}{s-5}~,~D:=\{s\in R|s\ne5\}$$
they are the same function

chrisplusian · Answer

lol I just remember a year or so ago when I had calc three..... we were doing lagrange multipliers and I ended up with a variable over the same variable..... I canceled them to one and my professor counted it wrong..... he gave me an in depth explanation as to why I could not do that. I really didn't get it becasuse I pointed out that even though it varied it would vary by the same amount always making it one. So I was afraid to do that here.... but I will give it a try and look at it after this professor posts homework solutions.... thank you :)

amistre64 · Answer

good luck :)  where are some equivalent functions that help when defining limits,  but equivalent is not indentical.

x/x  for example is not equal to 1 since it does not have x=0 in the Domain it creates a hole.  But limits do not care about value at a point, so we can use an equivalent (not equal) representation of it by filling in the hole.

in this case you are not finding an equivalent function to play with, you are just rewriting the function and the range and domain stay the same thruout.