Simplify the following expression

Simplify the following expression

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

高手可解答!

Update:

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

Update 2:

To 小路:

Absolutely WRONG!

The answer is n/(n+1)

But I need steps

Update 3:

To:小路

遲d我會將steps放上黎~你唔需要刪除答案 我會選你做最佳解答~

1 Answer

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  • Anonymous
    1 decade ago
    Favorite Answer

    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
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