Draw the graph of `f(x)=(x^2-5x+6)/(x^2-x)`

Explanation

`f(x)=((x-2)(x-3))/(x(x-1))`
f(x) is discontinous at x=0 and x=1
`underset(xrarr0lim) f(x) =+00` and `underset(xrarr1)lim f(x)=-00`
`underset(xrarr1)limf(x)-00` and `underset(xrarr00)lim f(x)=+00`
f(x) intersect the x axis the x axis at x =2 and x=3
`underset(xrarrpm00)lim(x^(2)-5x+6)/(x^(2)-x)`
Now `f(x) =(2x-5)(x^(2)-x)-(2x-1)(x^(2)-5x+6)/(x^(2)-x^(2))`
`=2(2x^(2)-6x+3)/(x^(2)-x^(2))`
`F(x)=0 rArr 2x^(2)-6x+3=0 "or" x =(3pmsqrt(3))/(2)`
Sign schem of f(x) is as follows
Clearly `x=(3+sqrt(3))/(2)` is point of minima and x =`(3-sqrt(3))/(2)`
is point of maxima
From the above information graph of y =f(x) is as shown in the following figure.