Solve the inequality:
(4x+3)/(x-1) ≤ 2
assuming x-1 > 0,
4x+3 <= 2x-2
x <= -5/2
But we assumed x>1, so no joy there.
If x-1 < 0, or x < 1,
4x+3 >= 2x-2
x >= -5/2
So, f(x) <=2 on the interval [-5/2,1)
See this at
http://www.wolframalpha.com/input/?i=%284x%2B3%29%2F%28x-1%29