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Question
Simplify `("n"^2 - 9)/(("n" + 3)!) + 6/(("n" + 2)!) - 1/(("n" + 1)!)`
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Solution
`("n"^2 - 9)/(("n" + 3)!) + 6/(("n" + 2)!) - 1/(("n" + 1)!)`
= `(("n" - 3)("n" + 3))/(("n" + 3)("n" + 2)("n" + 1)!) + 6/(("n" + 2)("n" + 1)!) - 1/(("n" + 1)!)`
= `1/(("n" + 1)!)[("n" - 3)/("n" + 2) + 6/("n" + 2) - 1]`
= `1/(("n" + 1)!)[("n" - 3 + 6 - "n" - 2)/("n" + 2)]`
= `1/(("n" + 2)("n" + 1)!)`
= `1/(("n" + 2)!)`
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