Can someone help me answer this question?

Question

If you add the denominator 3 to both the numerator and the denominator of the fraction 1/3 , the value of the fraction will double. Find a fraction that will triple the value when its denominator is added to its numeration and to the denominator.

If you add the denominator 3 to both the numerator and the denominator of the fraction 1/3 , the value of the fraction will double. Find a fraction that will triple the value when its denominator is added to its numeration and to the denominator.

Cant' figure it out

Answer 1

consider the general fraction
1/x

the first states that
((1+x)/(2*x))/(1/x)=2

(1+x)/2=2
1+x=4
x=3

Proves the first.

Solve the second
((1+x)/(2*x))/(1/x)=3
simplify
(1+x)/2=3
x=5

check
6/10=3/5 which is 1/5 tripled.

I went a bit further and looked at
the general fraction y/x
and the multiplication factor N

such that
((y+x)/(2*x))/(y/x)=N
solve for x
x=y*(2*N-1)

now you can find many fractions that meet the criteria.
set N=3 and vary y from 1 to 10
using excel, I get
N Y X

3 1 5
3 2 10
3 3 15
3 4 20
3 5 25
3 6 30
3 7 35
3 8 40
3 9 45
3 10 50



j