Composition of functions question.

I have f(x)= 3/(x=1) and g(x)=(x+5)/2.
I need to find f(g(x)). I know to set it up as (f(x)+5)/2, but I get the answer (5x+8)/(2x+2). The book says 6/(x+7) is correct. Could you please help?

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I assume you meant f(x) = 3/(x+1)).

Simple plug g(x) in for x in f(x):

f(g(x)) = 3/(g(x)+1))

= 3/([(x+5)/2]+1) (Note:((x+5)/2 + 1 = (x+5+2)/2 = (x+7)/2)
= 3/((x+7)/2)
= 6/(x+7)

Edit:typo

(x+5)/2+1
(7+x)/2=New denominator
3/(7+x)/2
=6/(7+x)
Domain: (-inf.,-7)U(-7,inf.)
Remember to find domain we look at the domain of g(x) and the f(g(x))