Question

the numerator of a rational number is 2 less than its denominator ,if the numerator is increased by 2 and the denominator is increased by 5
, the number becomes 1/2.find the rational number.

Answer 1

Let the numerator be n and denominator be d.
n=d-2 -------- (1)
Also, n+2/d+5=1/2
From (1),
d-2+2/d+5=1/2
d/d+5=1/2
2d=d+5
d=5
n=3
The fraction is 3/5

Answer 2

numerator = denominator -2
2+numerator , denominator +5 = 1/2

let numerator be x
2+x/x-2+5=1/2
2+x/x+3 = 1/2
2(2+x) = x+ 3
4+2x -x -3 = 0
x = -1
by substitution 
the number is -1/-1-2 = 1/3