lim_{n to 2} {2/x-2}-{8 x^{2} -4}

Lim x->2  2/(x-2) – 8/(x² – 4)
= lim x->2  2(x+2)/(x²-4)  – 8/(x² – 4)
= lim x->2  (2x+4)/(x² – 4)  – 8/(x² – 4)
= lim x->2  (2x + 4 – 8)/(x² – 4)
= lim x->2  (2x – 4)/(x² – 4)
= lim x->2  2(x – 2) / (x-2)(x+2)
= lim x->2  2/(x+2)
= 2/(2+2)
= 2/4
= 1/2