Evaluate the following limit: `underset( x rarr 3) ( "lim")(x^2-x-6)/(x^3-3x^2+x-3)`

Explanation

Given,

`(lim)_(x->3)(x^2−x−6)/(x^3−3x^2+x−3)`

`=(lim)_(x->3)((x-3)(x+2))/(x^2(x−3)+1(x−3))`

`=(lim)_(x->3)((x-3)(x+2))/((x−3)(x^2+1)`

`=(lim)_(x->3)((x+2)/(x^2+1))`

`=5/(10)`

`=1/2`