SOLUTION: In a certain positive fraction the denominator is greater than the numerator by 3 if 1 is subtracted from both the numerator and denominator the fraction is decreased by 1/14.find

Algebra ->  Finance -> SOLUTION: In a certain positive fraction the denominator is greater than the numerator by 3 if 1 is subtracted from both the numerator and denominator the fraction is decreased by 1/14.find      Log On


   

Question 1023155: In a certain positive fraction the denominator is greater than the numerator by 3 if 1 is subtracted from both the numerator and denominator the fraction is decreased by 1/14.find the fraction
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
Call the original fraction
x+%2F+%28x%2B3%29
Then we add one to top and bottom and get
%28x-1%29+%2F+%28x%2B2%29
This fraction is 1/14 less than the original...thus we have to solve
x+%2F+%28x%2B3%29+-+1%2F14+=+%28x-1%29+%2F+%28x%2B2%29
Now multiply everything by the lowest common denominator...

and we get
14x(x+2) - (x+2)(x+3) = 14(x+3)(x-1)
14x^2 + 28x - x^2 - 5x - 6 = 14x^2 + 28x - 42
The 14x^2 and 28x cancel out...
-x^2 - 5x - 6 = -42
x^2 + 5x + 6 = 42
x^2 + 5x - 36 = 0
(x + 9)(x - 4) = 0
x = -9 and x = 4
The original fraction must be
4/7.