can someone please explain

h t t p : / / w w w . j i s k h a . c o m / d i s p l a y . c g i ? i d = 1 2 5 7 0 4 1 1 4 5

division by zero is NOT allowed

(x+5)/(x-3) is valid for all x except x=3

but I can evalute using limits...

please

Whatever you did using limits is wrong.

The limit at x=3 exists if lim x→3- equals lim x→3+.

In this case, the two are not equal, because they tend toward inifinity in opposite directions, so the limit does NOT exist. Even if they tend toward infinity in the same direction, the limit does not exist.

Even in the case where the limit exists, as in the case of
f(x)=(x-3)*(x+5)/(x-3),
the point x=3 remains a hole in the domain of f(x).

In the case of f(x)=(x+5)/(x-3), there is no doubt that the point x=3 is excluded from the domain, which is ℝ\3.

Certainly! The link you provided is for a website called Jiskha.com, and it appears to be a specific page on that website. To understand what the link is pointing to, let's break it down:

- "http://" is the protocol used to transfer data over the internet.
- "www.jiskha.com" is the domain name of the website.
- "/display.cgi?id=1257041145" represents the specific resource or page on the website.

In this case, the resource is called "display.cgi" and it has a query parameter, "id", set to "1257041145". Query parameters are used to pass information to the server. Depending on how the website is designed, this particular query parameter might be used to retrieve specific content or data from the server.

To understand what exactly is displayed on that page, you would need to visit the link in a web browser and explore the content provided by the website.