Ответ:

Общий знаменатель — \(8r(8r+3)\):

\[\frac{1}{8r+3}+\frac{16r+9}{8r(8r+3)}=\frac{8r+16r+9}{8r(8r+3)}=\frac{24r+9}{8r(8r+3)}.\]

Ответ: \(\frac{24r+9}{8r(8r+3)}\).