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.)

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)