SOLUTION: (f/g)(x) f(x)=6/(x-3) and g(x)=2/(x+2) (g o f)(x)

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Question 261880: (f/g)(x) f(x)=6/(x-3) and g(x)=2/(x+2)

(g o f)(x)
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We are given the following functions:
f(x)=6/(x-3) and g(x)=2/(x+2)
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First we find: (f/g)(x)
(f/g)(x) = %286%2F%28x-3%29%29%2F%282%2F%28x%2B2%29%29
which is
(f/g)(x) =6%28x%2B2%29%2F%282%28x-3%29%29
or
(f/g)(x) =%283x%2B6%29%2F%28x-3%29
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Second, we find (g o f)(x)
this means put the f(x) function into the g(x) function as follows:
(g o f)(x) = %282%2F%28%286%2F%28x-3%29%29%2B2%29%29
which simplifies to
(g o f)(x) = %282%2F%28%286%2B2x-6%29%2F%28x-3%29%29%29
and then to
(g o f)(x) = 2%28x-3%29%2F%282x%29
and finally to
(g o f)(x) = %28x-3%29%2Fx