# Simplify the following expression

Simplify the following expression

{[1-(1/n)]/n-(1+n)[1-(1/n)} x 1/[n-(1/n)]

Update:

{[1-(1/n)]/n-(1+n)[1-(1/n)]} x 1/[n-(1/n)]

Update 2:

To 小路:

Absolutely WRONG!

But I need steps

Update 3:

To:小路

Rating
• Anonymous

Q: Simplify the following expression.

{[1-(1/n)]/n － (1+n)[1-(1/n)]} x 1/[n-(1/n)]

Sol:

{[1-(1/n)]/n － (1+n)[1-(1/n)]} x 1/[n-(1/n)]

＝ {[(n-1)/n]/n － (1+n)[(n-1)/n]} x 1/[(n²-1)/n]

＝ [(n-1)/n² － (n²-1)/n] x n/(n²-1)

＝ [(n-1)/n² － (n^3-n)/n²] x n/(n²-1)

＝ (n-1-n^3+n)/n² x n/(n²-1)

＝ - (n^3-2n-1)/n² x n/(n²-1)

＝ - (n^3-2n-1)/[n(n²-1)]

＝ - [(n+1)(n²-n-1)]/[n(n+1)(n-1)]

＝ - (n²-n-1)/(n²-n) ( 你可以只做到這個步驟 )

＝ - 1 ＋ 1/(n²-n)

Ans: - 1 ＋ 1/(n²-n)

2008-01-14 05:54:40 補充：

correction, from this step:＝ (n-1-n^3+n)/n² x n/(n²-1)＝ - (n^3-2n+1)/n² x n/(n²-1)＝ - (n^3-2n+1)/[n(n²-1)]＝ - [(n-1)(n²+n-1)]/[n(n+1)(n-1)]＝ - (n²+n-1)/(n²+n)Ans: - (n²+n-1)/(n²+n)

2008-01-14 05:56:00 補充：

correction, from this step:＝ (n-1-n^3+n)/n² x n/(n²-1)＝ - (n^3-2n+1)/n² x n/(n²-1)＝ - (n^3-2n+1)/[n(n²-1)]＝ - [(n-1)(n²+n-1)]/[n(n+1)(n-1)]＝ - (n²+n-1)/(n²+n) ( 你可以只做到這個步驟 )＝ - 1 ＋ 1/(n²+n)Ans: - 1 ＋ 1/(n²+n)

2008-01-14 06:01:45 補充：

I am sorry, I still get the different answer from yours.I try to substitute if n ＝ 2 to the questionit should be equal to - 5/6and substitute n ＝ 2 to my answerthe result is - 5/6

2008-01-14 06:02:11 補充：

but, substitute n ＝ 2 to your answerthe result is 2/3so, do you mind if check the question for me, please?

Source(s): 數學小頭腦