SOLUTION: the numerator of a fraction is one less than its denominator .if three is added to each of the numerator & denominator, the fraction is increased by 3/28. find its fraction

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Question 1094843: the numerator of a fraction is one less than its denominator .if three is added to each of the numerator & denominator, the fraction is increased by 3/28. find its fraction
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
the numerator of a fraction is one less than its denominator .
Denominator = D
Numerator = D-1
Original Fraction = %28D-1%29%2FD

if three is added to each of the numerator & denominator, 
New fraction = %28D-1%2Bred%283%29%29%2F%28D%2Bred%283%29%29 or %28D%2B2%29%2F%28D%2B3%29

the fraction is increased by 3/28. 
So also, New fraction = Original fraction + 3%2F28 or D%2F%28D-1%29%2B3%2F28 

So we set the two expressions for the New fraction equal:

%28D%2B2%29%2F%28D%2B3%29%22%22=%22%22%28D-1%29%2FD%2B3%2F28

LCD = 28D(D+3)

28D%28D%2B2%29%22%22=%22%2228%28D%2B3%29%28D-1%29%2B3D%28D%2B3%29

Solve that and get D=4 and D=-7

Only the positive answer works.  Fraction = 3/4

Edwin