The numerator of a fraction is 7 less than the denominator. If the numerator is increased by 2 and the denominator by 9,we again get the same fraction. Find the fraction.

Answer 1

n = d-7
(n+2)/(d+9) = n/d

(d-7+2)/(d+9) = (d-7)/d
d(d-5) = (d-7)(d+9)
d^2-5d = d^2+2d-63
7d = 63
d=9

check:
original fraction: 2/9
modified fraction: 4/18 = 2/9