TITLE: algebra help in AoCP intro to induction
QUESTION [1 upvotes]: In the introduction of mathematical induction, section 1.2.1 of Knuth's Art of Computer Programming, I'm struggling with (4) especially this relation:
$\phi^{n-2} +\phi^{n-1} = \phi^{n-2}(1+\phi)$
Looks like my algebra skills have gone all to rot, if I ever had any, so I am hoping someone can provide a detailed expansion of how these two forms are equal.

REPLY [1 votes]: Note that this is a purely algebraic result
that applies to any real, complex,
or other number that system
that 
has an identity,
is distributive
($a(b+c) = ab + ac$),
associative
($a(bc) = (ab)c$),
and commutative
($ab = ba$).
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