我與此人素不相識，提供答案，只是希望給所有網友大家參詳。如今記錄給删除，後來者未能參考，實有違此知識版之精神。
徵方法應付此類人。
曾向littlestar1022提供的答案：
Glad to see so many questions on Number Theory down here. My attempt on this question is as follow:
Assume the fraction of [(a+c)/(b+d)] could be further simplified.
Then there exists a common divisor “m” of (a+c) and (b+d) such that
(i)m is a positive integer;
(ii)m is greater than 1;
(iii)(a+c) = mp ; and (b+d)=mq for some integers p and q.
Given ab-cd=1 (or -1),
We have ab+bc-bc-cd=1 (or-1)
b(a+c)-c(b+d)=1 (or-1)
By (iii), mbp-mcq=1 (or -1)
m[bp-cq]=1(or-1)
[bp-cq]= (1/m) ( or – (1/m))
Since b, c, p and q are all integers, the left hand side of the equation [bp-cq] must be an integer too. However, the right hand side is (1/m) or (-1/m) which must not be an integer given that m is a positive integer greater than 1. Contradiction arises. Therefore, the assumption must be wrong. Hence the fraction of [(a+c)/(b+d)] could not be further simplified.
更新1:
不是我懂或不懂的問題，我所答者亦未必正確；而是此類人用心可疑。删除資料是不是不想其他人也可以參考這些資料。無論如何，myisland8132，多謝你的回覆。