How to solve ratio between two affine function

Dear expert:I want to maximize function called f(t)
f(t) = a1t+a2(1-t)/(b1t+b2t+b3t+c1(1-t)+c2(1-t)+c3(1-t))
s.t 0=<t<=1
(a1、a2、a3、b1、b2、b3、c1、c2、c3 just some values)
However, since the function I want to maximize is the division of two affline functions,so the error occurs.
I think there should be some special skills to deal with this problem, I would like to ask the experts to give me some advice,thank you!

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