Question

a fraction is such that numerator is 2 less than denominator.if you add 3 to numerator and5 to denominator resulting fraction is equivalent to original fraction

Answer 1

Let denominator be x and numerator will be x-2 (according to the given problem)
now add 3 to numerator and 5 to the denominator 
⇒x-2+3
  _____
  x+5 

Now this fraction is equal to the original fraction 
⇒x+1/x+5 = x-2/x
x²+x = (x+5) (x-2)
x²+x = x²-2x+5x-10
x²+x - x² +2x - 5x+10 = 0
-2x = -10
x = 5
Therefore the fraction is 
5 - 2/5 (substituting x value in x-2/5)
3/5.

Hope this helps you out.