If you start with a numerator N and a denominator that is 7 less then you have N / (N-7).

Now add 3 to each and you have (N+3) / (N-7+3) or (N+3) / (N-4) to simplify.

Now the result is 15/8 so you can set the numerators equal to each other (N+3)=15 and this results is N=12.

Same for the denominator (N-4)=8 also solves N=12.

Now to get the original fraction you plug 12 for N in the original formula of N / (N-7) and this gives you 12/5.

Good question!