can this only be evaluated to 0/8 or is there a way to algebraically manipulate it?

Question

Lim (x²-4)/(x²+4)

x->2

can this only be evaluated to 0/8 or is there a way to algebraically manipulate it?

Answer 1

I agree with Doug C.

Rational fractions are continuous except at 0's of the denominator.

That is lim as x->2 of the fraction is equal to the value of the fraction at 2, i.e. 0.

Note to Mark M.: your first comment only applies when the variable approaches infinity.

Answer 2

1) Since the degree is the same for both the limit is 1 approacing from the negative.

2) Use L'Hopital's Rule