let f(x)= (x / (6x-36)) and g(x)= (1/(x-6)). find all numbers x, if any, such that f(x) < g(x)
what's the trouble? Just, uh, do the math!
f(x) < g(x)
x/(6x-36) < 1/(x-6)
x/(6x-36) < 6/(6x-36)
as long as x>6, that means x<6
No joy there
If x<6, then x>6. Nope.
So, no solutions
See the graphs at
http://www.wolframalpha.com/input/?i=plot+y%3Dx%2F%286x-36%29+,+y%3D+1%2F%28x-6%29