SOLUTION: g(f(x)) when f(x) = (1-x)/x and g(x) = 1/(1+x) i know the answer is x because my frustration led me to substitute a couple of numbers in for x and my result was alway

Question 402101: g(f(x)) when f(x) = (1-x)/x and g(x) = 1/(1+x)

i know the answer is x because my frustration led me to substitute a couple of numbers in for x and my result was always whatever i plugged in for x. BUT i can't figure out how to do this without subbing in a number for x. HELP PLEASE?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
g(x) = 1/(1+x)
f(x) = (1-x)/x
---------
g(x) = 1/(1+x)
Sub f(x) for x
g(f(x)) = 1/(1 + (1-x)/x)
= 1/(x + (1-x)/x)
= 1/(1/x)
= x

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