The denominator of a fraction is 4 less than the numerator. if 3 is added to both nu, erator and denomiator the result is 3/2. find the sum of the numerator and the denominator of the orignal fraction

Let the numerator be x 
numerator =x 
denominator = x - 4
fraction = 

Add 3 to numerator and denomiator
numerator = x + 3
denominator = x -4 + 3 = x - 1
fraction = 

  = 

cross multiply:
2(x + 3) = 3(x - 1)
2x + 6 = 3x - 3
3x - 2x = 6 + 3
x = 9

Orignal fraction = 
= 
= 

Sum of the numerator and denominator = 9 + 5 = 14

This is too long-standing now get out