#### Answer

$\dfrac{27}{y^{2}-81}+\dfrac{3}{2(y+9)}=\dfrac{3}{2(y-9)}$

#### Work Step by Step

$\dfrac{27}{y^{2}-81}+\dfrac{3}{2(y+9)}$
Factor the denominator of the first fraction:
$\dfrac{27}{y^{2}-81}+\dfrac{3}{2(y+9)}=\dfrac{27}{(y-9)(y+9)}+\dfrac{3}{2(y+9)}=...$
Evaluate the sum of the two rational expressions and simplify:
$...=\dfrac{27(2)+3(y-9)}{2(y+9)(y-9)}=\dfrac{54+3y-27}{2(y+9)(y-9)}=...$
$...=\dfrac{3y+27}{2(y+9)(y-9)}=...$
Take out common factor $3$ from the numerator to provide a more simplified answer:
$...=\dfrac{3(y+9)}{2(y+9)(y-9)}=\dfrac{3}{2(y-9)}$