Hi people I have a math question that I can't solve in the way my teacher wants me to...it is:

*A fraction, after being simplified, is 2/3. If an integer is added to both the numerator and its denominator of this fraction, it becomes 8/11. If one is added to this integer, and the new integer is subtracted from both the numerator and the denominator of this fraction, it becomes 5/9. Find this fraction.*
Well I got the answer 24/36, but my teacher needs the "algebraic approach". Can anyone help? Thanks!