Question

The sum of numerator and denominator of a fraction is 3 less than twice the
the numerator and denominator. If each of the numerator and denominator decreased by 1, the fraction becomes 1/2 . Find the fraction.
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Answer 1

let numerator be x and denominator be y

as data,

x + y = 2xy _ 3.............. (1)

2(x _ 1) = y _ 1..............(2)

(2)......

2x _ 2 = y _ 1

y = 2x_ 1.........(3)

substitute (3) in (1)

x + 2x _ 1 = 2x(2x _ 1) _ 3

3x_ 1 = 4xsquare _ 2x _ 3

0= 4xsquare _ 5x _ 2

hints :

1. use the root formula as I don't know to type symbols

2. ,apply that value to y