We have the following:
When they tell us a certain number, we will assume a value x.
This number is added to the numerator and denominator of the fractional number 9/13 and gives us the result 9/11.
it is as follows
[tex]\frac{x+9}{x+13}=\frac{9}{11}[/tex]solving for x:
[tex]\begin{gathered} \frac{x+9}{x+13}=\frac{9}{11} \\ 11\cdot(x+9)=9\cdot(x+13) \\ 11x+99=9x+117 \\ 11x-9x=117-99 \\ 2x=18 \\ x=\frac{18}{2}=9 \end{gathered}[/tex]Therefore, the certain number is 9
