I want to know how to find the invariant factor decompostion of
If it is relevant, in a previous part of the question I found the primary decomposition to be
edit: forgot to mention that
Ok, so I'm guessing that is there because the denominator is the lowest common multiple of the original denominators. But how did you find the other 2 terms? They appear to have the same product as the first set of denominators, is that relevant?
I was going through my notes for a different question and found a worked example. On the off chance that somebody else was wondering about this also, the method is to take the highest power for each term and multiply them and then the next highest power for each term and so on until you run out of terms. So in this case we have:
Taking the highest power of each term gives
and leaves us with
Taking the highest powers remaining gives
and leaves
So the invariant factor decomposition is