Integer and fractional part : propfrac

propfrac takes as argument a rational fraction.
propfrac rewrites this rational fraction as the sum of it's integer part and proper fractional part.
propfrac(A(x)/B(x)) writes the fraction ${\frac{{A(x)}}{{B(x)}}}$ (after reduction), as :

Q(x) + $${\frac{{R(x)}}{{B(x)}}}$$     where R(x) = 0 or 0 $$\leq$$ degree(R(x)) < degree(B(x))

Input :

propfrac((5*x+3)*(x-1)/(x+2))

Output :

5*x-12+21/(x+2)