lim x2(squared) - 6x + 8 / 2x2(squared) - 32
x-4 (the - is an arrow)

the easiest way is always L'ohspitals Rule:
Take the derivative of the numerator and denominator and substitute x, in this case:

lim (x^2 - 6x +8)/2x^2 - 32 = lim (2x -6)/4x = 2/16 = 1/2
x->4

the easiest way is always L'ohspitals Rule:
Take the derivative of the numerator and denominator and substitute x, in this case:

lim (x^2 - 6x +8)/2x^2 - 32 = lim (2x -6)/4x = 2/16 = 1/2
x->4

Right, except 2/16 = 1/8, not 1/2.

Right, except 2/16 = 1/8, not 1/2.
LoL, thanks for correcting

\lim_{x\to 4}\frac{x^{2}-6x+8}{2x^{2}-32}

If I may, L'Hopital is not needed in this case. But it works OK.

We are only dealing with a rational function.

Notice we can factor:

\lim_{x\to 4} \;\ \frac{(x-4)(x-2)}{2(x-4)(x+4)}=\lim_{x\to 4} \;\ \frac{(x-2)}{2(x+4)}=\frac{1}{8}

Thank you Galactus.