Umformung von (1 + 6n + 2n2 )/((n + 3)n) zu [ 1 / (n(n + 3)) ]+ 2?

Question

an = 1 + 6n + 2n² /(n + 3)n = [ 1 / n(n + 3) ]+ 2.

EDIT(Lu): Gemeint ist gemäss Antwort

an = (1 + 6n + 2n² )/((n + 3)n) = [ 1 / (n(n + 3)) ]+ 2.

Answer 1

1 +6n +2 n^2=  2n(n+3) +1 (Zähler umformen)

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= (2n(n+3) +1 )/( n(n+3))

allgemein gilt: (A+B)/C = A/C +B/C

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=(2n(n+3))/( n(n+3))  + 1/( n(n+3))

------------->Kürzen des 1. Summanden

= 2 + 1/( n(n+3))