The denominator of a fraction is three more than the numerat

The denominator of a fraction is three more than the numerator. If both numerator and denominator are increased by nine, the simplified result is 13/14. Find the original fraction. (Do NOT simplify.)

Solution

let the original fraction be a/b

given denominator is 3 more than numerator =>b =a+3

==>fraction ia a/(a+3)

given both numerator , denominator increased by 9

==>fraction ia (a+9)/(a+3 +9)

==>fraction ia (a+9)/(a+12)

equals to 13/14

(a+9)/(a+12) =13/14

cross multiply

14(a-9)=13(a+12)

14a -126=13a +156

14a-13a=126+156

a =282

b =a+3

=>b =282+3

=>b=285

fraction is 282/285