Question 846412
The denominator of the example was factored so that the undefined values of x could be identified.  The 7 appears as a factor on one of the terms of the general polynomial; but it does NOT appear in the factorization.  


The question of "what is the domain", requires knowing for what values of x in the rational function is defined and for what values of x the function is undefined.  Division by zero is impossible, so you want to find which values of x in the denominator would make the denominator equal to zero.  x must not be values which make the denominator equal to zero.


Properly written, your given function is  {{{f(x) = (8x^2+2x-3)/(x^2-4x)}}}
The grouping symbols are necessary when using pure text, even if you have the rendering tags.  LOOK AT THE DENOMINATOR!  This must be nonzero.  The domain of f will be the real values of x for which {{{x^2-4x<>0}}}.