Bonjour,
[tex] x^2-4x+3\ge\frac{x-3}{x-1} [/tex]
[tex] x^2-4x+3-\frac{x-3}{x-1}\ge0 [/tex]
[tex] \frac{(x-1)(x^2-4x+3)-(x-3)}{x-1}\ge0 [/tex]
[tex] \frac{(x-1)(x-3)(x-1)-(x-3)}{x-1}\ge0 [/tex]
[tex] \frac{(x-3)[(x-1)^2-1]}{x-1}\ge0 [/tex]
[tex] \frac{x(x-3)(x-2)}{x-1}\ge0 [/tex]
...........0.......1.........2..........3...........
x ------0++++++++++++++++++++++
x-1 ------------0+++++++++++++++++
x-2 ---------------------0++++++++++++
x-3 -------------------------------0++++++
============================
++0------|+++++0-------0++++++
=>]-oo 0] U ]1 2] U [3 +oo[
