Substitutions

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Substitutions

by Buix0065 » Sun Jul 31, 2011 10:32 am
((n - 2)^-1)(2 + n)

If n >2 and 2/n is substituted for all instances of n in the above expression, then the new expression will be equivalent to which of the following:

A) (n + 1)(n - 1)^-1
B) -(n + 1)(n - 1)^-1
C) -(n - 1)(n + 1)^-1
D) ((2 + n)^-1)(n - 2)
E) ((n - 2)^-1)(2 + n)

[spoiler]OA: B i originally chose 4 for n, thinking that 1/2 would be easier to work with than 2/3 (in the case of choosing 3) only to find that 4 returns -1 to the original equation and -5/3 for the answer B. Any thoughts on avoiding this sort of issue in the future when picking numbers?

Thanks![/spoiler]
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by edge » Sun Jul 31, 2011 1:37 pm
Original expression is simplified to (n+2)/(n-2). Substitute '2/n' for 'n', and you get (2+2n)/(2-2n) = (1+n)/(1-n). Therefore B is the answer.