I want represent the fraction $$\frac{a+b+a b c+a b d}{1+a c+b c+a d+b d+a b c d}\qquad\qquad\qquad (1)$$ as a continued fraction. Here $a,b,c,d$ free variables.
I could only get $$\frac{a+b+a b c}{1+b c+a d+b d+a b c d}=\frac{1}{d+\frac{1}{a+\frac{1}{c+\frac{1}{b}}}}$$ However, I cannot repersent the original expression (1).