Question 261880
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) = {{{(6/(x-3))/(2/(x+2))}}}
which is
(f/g)(x) ={{{6(x+2)/(2(x-3))}}}
or
(f/g)(x) ={{{(3x+6)/(x-3)}}}
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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) = {{{(2/((6/(x-3))+2))}}}
which simplifies to
(g o f)(x) = {{{(2/((6+2x-6)/(x-3)))}}}
and then to
(g o f)(x) = {{{2(x-3)/(2x)}}}
and finally to 
(g o f)(x) = {{{(x-3)/x}}}