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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)
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25 Jan 2023, 23:18
25 Jan 2023, 23:18
Expert Reply
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Question Stats:
100% (02:21) correct
0% (00:00) wrong based on 4 sessions
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If \(x\neq{-1}\) , \(\frac{1- x^{16}}{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)}\) is equivalent to
A. -1
B. 1
C. x
D. 1-x
E. x-1
A. -1
B. 1
C. x
D. 1-x
E. x-1
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8)
[#permalink]
28 Jan 2023, 09:14
28 Jan 2023, 09:14
Expert Reply
Numerator
\(1 - x^{16}\)
\(= (1 + x^8) (1 - x^8)\)
\(= (1 + x^8) (1 + x^4) (1 - x^4)\)
\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 - x^2)\)
\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)\)
Denominator
\((1 + x^8) (1 + x^4) (1 + x^2) (1 + x)\)
Expanded / simplified equation would be
\(\frac{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)}{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x)}\)
= 1 - x
Answer: D
\(1 - x^{16}\)
\(= (1 + x^8) (1 - x^8)\)
\(= (1 + x^8) (1 + x^4) (1 - x^4)\)
\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 - x^2)\)
\(= (1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)\)
Denominator
\((1 + x^8) (1 + x^4) (1 + x^2) (1 + x)\)
Expanded / simplified equation would be
\(\frac{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x) (1 - x)}{(1 + x^8) (1 + x^4) (1 + x^2) (1 + x)}\)
= 1 - x
Answer: D
gmatclubot
Re: If x#-1, x^16/{(1+x)*(1+x^2)*(1+x^4)*(1+x^8) [#permalink]
28 Jan 2023, 09:14
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