Simplify: $(\frac{13}{15}-\frac{3}{5})÷(\frac{13}{15}+\frac{3}{5})$

We have,

$(\frac{13}{15}-\frac{3}{5})÷(\frac{13}{15}+\frac{3}{5})$

$=\left(\frac{13-9}{15}\right)÷\left(\frac{13+9}{15}\right)$

$=\left(\frac{4}{15}\right)÷\left(\frac{22}{15}\right)$

$=\frac{\frac{4}{15}}{\frac{22}{15}}$

$=\frac{4}{22}$

$=\frac{2}{11}$

Hence, this is the answer.