if the denominator was not changed then it would still be three. So the 2 would change so let’s make the original numerator an x because we don’t know it.

So it’s x/3 – 9/1= 2/3

x/3 -9/1 + 9/1= 2/3 +9/1

2+9

over

3+1

equals

11/3

let x = the odd integer, then x+2 is the next odd integer, so the fraction can be shown as x / (x+2) (parenthesis for clarification)

now (x-9) / (x+2) = 2/3 subtracting 9 from the numerator

solving by cross multiplying

3(x+9) = 2 (x+2)

3x + 27 = 2x + 4

x = 31

fraction thus becomes 31/33

subtracting 9 from the numerator is 22/33 which is in the ration of 2/3 so answer checks out.

hope explaination helps