Question 285968
I think you're confused about what 
is a factor and what's not.
Suppose you had this fraction:
{{{(6*6*6*11*11*11*11)/(377*11*11*11*11)}}}
The 4 11's on top- cancel the 4 11's
on the bottom.
Now suppose you had
{{{(6*6*6*(x-11)*(x-11)*(x-11)*(x-11))/(377*(x-11)*(x-11)*(x-11)*(x-11))}}}
You've still got 7 factors on top and 5 factors on the bottom
Each of the {{{x-11}}}'s is a factor and the 4 on the bottom cancel the 4 on the top.
Your problem is:
{{{(x-4)/(x^2 - 3x - 4)}}}
The bottom factors to
{{{(x - 4)*(x +1)}}} so, you have
{{{(x-4)/((x-4)*(x+1)) = 1/(x+1)}}} 
If your problem is factoring the denominator, you just
have to keep backtracking until you clear up all confusions