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Given a positive integer n, the rational number r satisfies

2n/n - 2n/(n + 1) = r*2n/n.

 

Express r in terms of n.  (Your expression should be as simplified as possible.)

 Apr 7, 2023
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Solve for r:
2 - (2 n)/(n + 1) = 2 r


order to isolate r to the left hand side.


2 - (2 n)/(n + 1) = 2 r is equivalent to 2 r = 2 - (2 n)/(n + 1):


2 r = 2 - (2 n)/(n + 1)


Divide both sides by 2:


r = 1 /(n + 1)

 Apr 8, 2023

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