We are given the following expression
[tex]13+(\frac{5}{9}-\frac{4}{9})[/tex]Since the denominator of the fractions are the same, we can simply subtract the numerators as
[tex]\begin{gathered} 13+(\frac{5}{9}-\frac{4}{9}) \\ 13+(\frac{5-4}{9}) \\ 13+\frac{1}{9} \end{gathered}[/tex]Finally, add them together
[tex]\begin{gathered} 13+\frac{1}{9} \\ \frac{9\cdot13+1}{9} \\ \frac{117+1}{9} \\ \frac{118}{9} \end{gathered}[/tex]Therefore, the simplified expression is 118/9
[tex]13+(\frac{5}{9}-\frac{4}{9})=\frac{118}{9}[/tex]