SOLUTION: Please help me figure this out. f(x) = (1-x)/5x, g(x) = 1/(1+5x) I am solving for g(f(x)) and f(g(x)) I started and got confused with the denominator and can't seem to reduce

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Question 950938: Please help me figure this out.
f(x) = (1-x)/5x, g(x) = 1/(1+5x)
I am solving for g(f(x)) and f(g(x))
I started and got confused with the denominator and can't seem to reduce the denominator properly. I started with f(g(x)) and got (1-(1/1+5x) / 5(1/(1+5x) and am totally confused. Could someone please explain how to do this?
Found 3 solutions by josgarithmetic, stanbon, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!

'

'
-------complex fraction

You learned what to do about a complex fraction in your previous algebra course. In this example, multiply by 1 in the form of . Simplify.

Done correctly, this should be .

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
f(x) = (1-x)/5x, g(x) = 1/(1+5x)
I am solving for g(f(x)) and f(g(x))
------
g[f(x)] = g[(1-x)/5x] = 1/[1 + 5[(1-x)/5x]]
------
= 1/[1+(1-x)/x]
------
= 1/[x + 1-x]/x
------
= 1/(1/x)
====
= x
------------------------------
Note:: f(x) = [1/5x]-[1/5]
----------------------
f[g(x)] = f[1/(1+5x)] = [1/[5[1/(1+5x)]-[1/5]
-----
= [1/[5/(1+5x)] - [1/5)
= [(1+5x)/5] - [1/5]
= [1+5x-1]/5
= 5x/5
= x
===============
Cheers,
Stan H.
-----------------

Answer by MathTherapy(10553)   (Show Source):
You can put this solution on YOUR website!

Please help me figure this out.
f(x) = (1-x)/5x, g(x) = 1/(1+5x)
I am solving for g(f(x)) and f(g(x))
I started and got confused with the denominator and can't seem to reduce the denominator properly. I started with f(g(x)) and got (1-(1/1+5x) / 5(1/(1+5x) and am totally confused. Could someone please explain how to do this?

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