You can formulate this with algebra.

If the original numerator is x, then the denominator will be 3x-1.

Next add two to both these, leaving us with x+2 as numerator and 3x+1 as denominator. Now rewrite these as a fraction and equate to 1/2.

Now solve

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

2x+4 = 3x+1

x=3

You can now resubstitute into original equations for numerator and denominator, giving a fraction of 3/8.

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