Question

The numerator of a fraction(which is a positive integer) is 1 less than the denominator. The sum of the fraction and two times its reciprocal is 41/12. What is the numerator and the denominator? P.s

Answer 1

`3` and `4`

Explanation:

Writing `n` for the integer numerator, we are given:

`n/(n+1) + (2(n+1))/n = 41/12`

Note that when we add fractions we first give them a common denominator. In this case we naturally expect that denominator to be `12`.

Hence we expect both `n` and `n+1` to be factors of `12`.

Try `n=3`...

`3/4+8/3 = (9+32)/12 = 41/12" "` as required.