Fully evaluate the following definite integrals. $(6$ points each$)$

$($a$)$

${\displaystyle \underset{-2}{\overset{1}{}}}\frac{x-3}{(x-2)(x-4)}dy$

$($b$)$

${\displaystyle \underset{0}{\overset{ln(2)}{}}}\frac{e^x}{\sqrt[\phantom{2}]{9-e^{2x}}}dx$