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]Find the sum of all values of n that satisfy 1/n-1 + 1/n+1 = 3/n

help is appreciated.

 Nov 25, 2020
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Find the sum of all values of n that satisfy 1/n-1 + 1/n+1 = 3/n

help is appreciated.

 

Hello Guest!

 

\(\color{BrickRed}1/n-1 + 1/n+1 = 3/n\\ \frac{2}{n}=\frac{3}{n}\\ n⇒\pm\infty \)

The function has no zero.

Because point calculation comes before line calculation,

you have to put the divisors in brackets.

 

\(1/(n-1) + 1/(n+1) = 3/n\)

\(\frac{1}{n-1}+\frac{1}{n+1}=\frac{3}{n}\\ \frac{n^2+n+n^2-n}{n(n^2-1)}=\frac{3(n^2-1)}{n(n^2-1)}\\ 2n^2=3n^2-3\\ n^2=3\\ n=\pm \sqrt{3}\)

\(n\in\{-\sqrt{3},\sqrt{3}\}\)

laugh  !

 Nov 26, 2020

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