Question

the denominator of a fraction exceeds the numerator by 2.if 5 be added to the numerator the fraction increases by unity

Answer 1

Let n = numerator
then from "denominator of a fraction exceeds the numerator by 2" we have
n+2 = denominator
.
We derive our equation from:"If 5 be added to the numerator the fraction increases by unity":
(n+5)/(n+2) = n/(n+2) + 1
multiplying both sides by (n+2)
(n+5) = n + (n+2)
n+5 = 2n + 2
5 = n + 2
3 = n (numerator)
.
Denominator:
n+2 = 3+2 = 5
.
Solution then is numerator/denominator: 3/5