You try to look for a factorization of the numerator, but not immediately recognizing factorizations for 119, polynomial division or synthetic division seem better.
v -8
_______________________________
|
v-8 | v^2 -16v 119
|
| v^2 -8v
--------------
0 -8v 119
-8v -64
-------------
0 183
The complete quotient here is .