Simplifying G1(1+F1)/(1+G1F2(1+F1)) with feedback terms

[magnifik]

I am trying to simply G₁ = G₁(1+F₁) / (1 + G₁F₂(1+F₁)) in terms of G₁, G₂, H₂, and H₃ where F₁ = G₂/(1-G₂H₂) and F₂ = G₃ / (1-G₃H₃)

i got the result
(G₁(1-G₂H₂)(1-G₃H₃) + G₁G₂(1-G₃H₃)) / ((1-G₂H₂)(1-G₃H₃) + G₁G₃(1-G₂H₂) + G₁G₂G₃)

however, the book gives the result with a +1 in the denominator so their denominator is 1 + (1-G₂H₂)(1-G₃H₃) + G₁G₃(1-G₂H₂) + G₁G₂G₃

i did the problem 3 times and got the same answer. is the solution in the book a typo, or am i doing something wrong?

 

[Ray Vickson]

I am trying to simply G₁ = G₁(1+F₁) / (1 + G₁F₂(1+F₁)) in terms of G₁, G₂, H₂, and H₃ where F₁ = G₂/(1-G₂H₂) and F₂ = G₃ / (1-G₃H₃)

i got the result
(G₁(1-G₂H₂)(1-G₃H₃) + G₁G₂(1-G₃H₃)) / ((1-G₂H₂)(1-G₃H₃) + G₁G₃(1-G₂H₂) + G₁G₂G₃)

however, the book gives the result with a +1 in the denominator so their denominator is 1 + (1-G₂H₂)(1-G₃H₃) + G₁G₃(1-G₂H₂) + G₁G₂G₃

i did the problem 3 times and got the same answer. is the solution in the book a typo, or am i doing something wrong?

I used Maple (a computer algebra system) to do the question and got your answer exactly. Either the book is wrong or you copied something incorrectly.

RGV