How do you determine the limit of $\frac{x + 4}{x - 4}$ $(x+4)/(x-4)$ as x approaches 4+?

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Answer 1 · 2016-07-11T23:13:00

$lim_(x->4^+) (x+4)/(x-4) = oo$

$lim_(x->4^+) (x+4) = 8$

$therefore 8lim_(x->4^+) 1/(x-4)$

As $lim_(x->4^+) (x-4) = 0$ and all points on the approach from the right are greater than zero, we have:

$lim_(x->4^+) 1/(x-4) = oo$

$implies lim_(x->4^+) (x+4)/(x-4) = oo$

How do you determine the limit of (x+4)/(x-4)x+4x−4(x+4)/(x-4) as x approaches 4+?