Question

in a certain positive fraction the denominator is greater than numenator by 3. if 1 is substracted from both the numenator and denominator the fraction is decreased bi 1/14 .find the fraction

Answer 1

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.