Answer
$\displaystyle \frac{y+5}{y-4}$
Work Step by Step
To subtract rational expressions with the same denominator,
subtract numerators and place the difference over the common denominator.
If possible, factor and simplify the result.
---
Don't forget to place the second numerator in parentheses when subtracting.
$\displaystyle \frac{2y^{2}+6y+8}{y^{2}-16}-\frac{y^{2}-3y-12}{y^{2}-16}= \displaystyle \frac{2y^{2}+6y+8-(y^{2}-3y-12)}{y^{2}-16}$
$= \displaystyle \frac{2y^{2}+6y+8-y^{2}+3y+12}{y^{2}-16}$
$= \displaystyle \frac{y^{2}+9y+20}{y^{2}-16}\qquad$... factor what we can...
... Numerator:
... two factors of $c=20$ whose sum is $9$... are $+4$ and $+5$.
$y^{2}+9y+20=(y+4)(y+5)$
... Denominator: a difference of squares, $(y)^{2}-4^{2}$
$=\displaystyle \frac{(y+4)(y+5)}{(y+4)(y-4)}$
... reduce (divide the numerator and denominator with common factors)
$=\displaystyle \frac{y+5}{y-4}$
