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lim  x →3   [  x^2 - 2x - 3 ] / [ x  -3  ]              factor the numerator

lim x → 3     [ (x + 1) (x - 3) / [ x - 3 ]

lim x →  3       x +  1       =     4

$\lim_{x\rightarrow 3}x^2-2x-3/x-3=(x-3)(x+1)/(x-3)=(x+1)/1=4$