\[\frac{3c + 7}{c^{2} + 7c} + \frac{c - 7}{7c + 49} =\]
\[= \frac{3c + 7}{c(c + 7)} + \frac{c - 7}{7 \cdot (c + 7)} =\]
\[= \frac{21c + 49 + c^{2} - 7c}{7c(c + 7)} =\]
\[= \frac{c^{2} + 14c + 49}{7c(c + 7)} =\]