help me pleasee :(( (Rational equalities and inequalities)

Question

The denominator of a fraction is 1 more than thrice the numerator. If the numerator is doubled, and the numerator is tripled, the result will be 4/21. What is the fraction?

Answer 1

d = 3n + 1

4/21 = 2(3)n/(3n+1) if you really meant the numerator is doubled, and then tripled

12n + 4 = 126n

114n = 4

n=4/114 and d = 3n+1 = 12/114 + 1 = 126/114

but that seems unlikely, as it has a fractional numerator and fractional denominator.

so maybe you meant double the numerator and triple the denominator?

then

4/21 = 2n/3(3n+1)

36n+12 = 42n

6n=12 n=12/6 = 2

and d = 3n+1 = 7

so the original fraction was 2/7