Let the numerator and denominator be p and q respectively.
Then, (p + 2) / (q + 3) = 7/9
⇒ 9(p + 2) = 7(q +3)
⇒ 9p - 7q = 3 ....(i)
Again, (p - 1) / (q - 1) = 4/5
⇒ 5p - 4q = 1 ....(ii)
Solving (i) and (ii) we get,
p = 5, q = 6
Required fraction = 5/6
