Question 973315
Expect two of them, because no common factor should occur between numerator and denominator.


(I had a comment here about Discriminant, but changed my mind.)


{{{R(x)=((3x+1)(x-1))/((2x-1)(x+2))}}}
As already stated, no common factors.    The vertical asymptotes are for denominator zero as when x=1/2  or x=-2.