The numerator of a simple fraction is 2 less than its denominator. The sum of this fraction and its reciprocal is 2 4/35. Find this fraction.

1 answer

n = d-2
n/d + d/n = 2 4/35

substitute in for n and we have

(d-2)/d + d/(d-2) = 74/35
d = 7
so, n=5

check:

5/7 + 7/5 = (25+49)/35 = 74/35