def dzt(p,q,x=x):
    T=PolynomialRing(QQ,1,'x')
    x=var('x')
    q=q*x^0
    q=q.full_simplify()
    p=p*x^0
    p=p.full_simplify()
    l=list(T(q).factor())
    h3=1
    h4=1
    for n in range(len(l)):
        h3=(h3*l[n][0])^(l[n][1]-1)
    for n in range(len(l)):
        h4=(h4*l[n][0])
    k=h4.degree()+h3.degree()
    if (h3.degree()==1):
        h1=A0
    else:
        A=var(['A%d' %n for n in range(h3.degree())])
        h1=sum([A[n]*(x^n) for n in range(h3.degree())])
    if (h4.degree==1):
        h2=B0
    else:
        B=var(['B%d' %n for n in range(h4.degree())])
        h2=sum([B[n]*(x^n) for n in range(h4.degree())])
    h=(diff((h1/h3),x)+h2/h4-p/q)
    h=h.full_simplify()
    m=[]
    for n in range(k+len(l)):
        if (q.subs(x=n))!=0:
            m=m+[n]
    v=A+B
    y=solve([h.subs(x=m[n]) for n in range(k)],v)
    h1=h1.subs(y[0])
    h2=h2.subs(y[0])
    d=denominator(h2)
    h2=h2*denominator(h2)
    C=PolynomialRing(RR,1,'x')
    h2=C(h2)
    h4=C(h4)
    h1=h1/h3
    h2=h2/h4
    C.<w>=RR[]
    h2=h2.subs(x=w)
    z1=h2.partial_fraction_decomposition()
    z=0
    for n in range(len(z1[1])):
        z=z+integral(z1[1][n],w)
    z=z.subs(w=x)
    f=h1+z/d
    f=f.subs(x=x)
    return f