Let the numerator be x
numerator =x
denominator = x - 4
fraction = [tex] \frac{x}{x-4} [/tex]
Add 3 to numerator and denomiator
numerator = x + 3
denominator = x -4 + 3 = x - 1
fraction = [tex] \frac{x+ 3}{x - 1} [/tex]
[tex] \frac{x+ 3}{x - 1} [/tex] = [tex] \frac{3}{2} [/tex]
cross multiply:
2(x + 3) = 3(x - 1)
2x + 6 = 3x - 3
3x - 2x = 6 + 3
x = 9
Orignal fraction = [tex] \frac{x}{x -4} [/tex]
= [tex] \frac{9}{9-4} [/tex]
= [tex] \frac{9}{5} [/tex]
Sum of the numerator and denominator = 9 + 5 = 14
