What's the next step in showing that f(g(x)) = x?

f(x) = (x - 9)/(x + 5)
g(x) = (-5x - 9)/(x - 1)

I got this far "f(g(x)) = (((-5x - 9)/(x - 1)) - 9) / (((-5x - 9)/(x - 1)) + 5)" and got stuck.

Question

What's the next step in showing that f(g(x)) = x?

f(x) = (x - 9)/(x + 5)
g(x) = (-5x - 9)/(x - 1)

I got this far "f(g(x)) = (((-5x - 9)/(x - 1)) - 9) / (((-5x - 9)/(x - 1)) + 5)" and got stuck.

anonymous · Answer

@primeralph

anonymous · Answer

f(g(x)) = (g(f(x) - 9) / (g(x) + 5)
f(g(x)) = (((-5x - 9)/(x - 1)) - 9) / (((-5x - 9)/(x - 1)) + 5)
I have no idea what comes after that part... and then
f(g(x)) = x

primeralph · Answer

just do the normal common factor etc

anonymous · Answer

?

primeralph · Answer

just go on............it'll fall out nicely

anonymous · Answer

I'm completely stuck. No idea what happens after that part.

primeralph · Answer

find the common denominators etc stuff like that.|dw:1368763119471:dw|