Question 1180773
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<pre>

The function is  {{{((x+2)*(x-3))/abs(x-3)}}}.


In vicinity of  x= 3, the function is simply  +/- (x+2),

where the sign  " + "  works on the right of x= 3

and   the sign  " - "  works on the  left of x= 3.



Thus the limit is 5 from the right side and  -5 from the left side.


The function is DISCONTINUOUS at x = 3,  so the two-sided limit DOES NOT exist.



                        <U>Visual check</U>



    {{{graph( 400, 400, -10, 10, -10, 10,        
              ((x+2)*(x-3))/abs(x-3)
)}}}


                  Plot y = {{{((x+2)*(x-3))/abs(x-3)}}}
</pre>

Solved, answered, explained and checked.