Let the denominator of the fraction be x
Numerator is 2 times less than denominator. Therefore The fraction we get is -
x-2/x
After adding 3 to numerator and 5 to the denominator resulting fraction is equals to the original fraction -
therefore -
x-2+3/x+5 = x-2/x
x+1/x+5 = x-2/x
Now by cross multiplication
(x+1)(x) = (x-2)(x+5)
x^2 + x = x^2 + 5x - 2x - 10
x = 5x - 2x - 10
x = 3x - 10
x - 3x = -10
-2x = -10
x = -10/-2
x = 5