You can put this solution on YOUR website! f(x)=(2x-3)/(x-2)
at infinity (-) the function is +2
at x=3/2 the function is 0
at x=2, the function is undefined, and it is negative infinity from the left and positive infinity from the right
at infinity (+) the function is +2.
so from (-oo, 3/2) the function is decreasing from 2 to 0
from ((3/2) to 2), the function is decreasing from 0 to -oo.
from (2, +oo), it is again decreasing.
There is a discontinuity at x=2.
There is no place where it is continuous and increasing.
