$(4$ points$)$ Use the limit comparison test to determine whether each of the following series converges or diverges. Include all relevant work.

$($a$){\displaystyle \underset{k=!}{\overset{}{}}}\frac{4+8k}{7k^{\frac{3}{2}}+k}$

$($b$){\displaystyle \underset{k=1}{\overset{}{}}}\frac{2+3^k}{4^k+3^k}$