dear sir ,
I'm asking about the table of variation
for function
( e^2x - 3.e^x +2) / ( e^2x + 3.e^x - 4 )

and I need the shape of graph representing this function

You have to do that yourself. Have some values of 'x' like for example -10, -5, -2.5, -2, -1.5, -1, -0.5, 0, 0.5, 1, 1.5, 2, 2.5, 5, 10. That makes 15 points of reference. Have graph paper and plot the points, join them and you'll have the shape of your graph.

You can go to Online 2d function plotter f(x) and put in ( exp(2*x) - 3*exp(x) +2) / ( exp(2*x) + 3*exp(x) - 4 ).