SOLUTION: the numerator of a certain fraction exceeds its denominator by 2, and the fraction itself exceeds its reciprocal by 24/35. find the fraction

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Question 910300: the numerator of a certain fraction exceeds its denominator by 2, and the fraction itself exceeds its reciprocal by 24/35. find the fraction
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

%28d%2B2%29%2Fd+=+d%2F%28d%2B2%29+%2B+24%2F35 |Multiplying thru by 35d(d+2) so as all denominators = 1

35(d+2)^2 = 35d^2 + 24d(d+2)

35d^2 + 140d + 140 = 35d^2 + 24d^2+48d

24d^2 - 92d - 140 = 0

6d^2 - 23d - 35 = 0 (Tossing out the negative solution for unit measure)

(6d +7)(d-5) = 0

d = 5

Fraction is 7/5