documentclass{article}

usepackage{xcolor}
usepackage{mathtools, bm}

begin{document}

 begin{alignat*}{2}
  f_1(x,y,z)&=x^3yz^5+1 &enspace smash{rule[-13em]{0.5pt}{14em}}& enspace g(x,y,z)=3x^5y^2z - x y^3z + 7yz + 18 \
  cline{4-4}
   f_2(x,y,z)&=yz+1 \[-1.5ex]
    & & & enspace g(x,y,z)-3x^5yf_2(x, y, z) \[-2ex]
   cline{4-4}
 & & & enspace =3x^5y^2z - x y^3z + 7yz + 18 -3x^5y(yz+1) \
 pi_1(x, y, z) & \[-1.5ex]
  & & & enspace =3x^5y - x y^3z + 7yz + 18 \[-2ex]
   cline{4-4}
 pi_2(x, y, z) & =3x^5y \[-1.5ex]
  & & & enspace - x y^3z + 7yz + 18 \[-1.5ex]
v(x, y, z) & = color{red}{bm{-3x^5y}}
  end{alignat*}

end{document}