Question

I'm working my way through Paul's Online Notes and on page http://tutorial.math.lamar.edu/Classes/Alg/PartialFractions.aspx Example 1(c) I don't understand why the LCN includes (x-2) as well as (x-2)^2 Thanks.

Answer 1

it's a special case

Answer 2

I don't know the exact explanation, but you have to do that if you have a squared factor

Answer 3

you have to account for all the possible linear combinations

Answer 4

(x-2) is one possible denominator in the setup, but does not account for an (x-2)^2 in the original work

Answer 5

spose you were adding the fractions:\[\frac{a}{7}+\frac{b}{3}+\frac{c}{49}\]
just because 7*7 = 49 does not mean that the decomposition would not have a denom of 49 ...