Question

Is this two equal?
\[(x+1)\] and \[\frac{(x+1)(x+2)}{(x+2)}\]
Yes, it might sound like a stupid question but it is undefined at x=-2 (or is it?).

Answer 1

At x=-2 there is a hole in the graph of the second. But for first it's not so:)
The second is defined at x=-2 but their's hole

Answer 2

Then they are not equal as \[(x+1) \neq \frac{(x+1)(x+2)}{(x+1)} \ \text{when } x=-2\]

Answer 3

Let me check once

Answer 4

Yeah the domain of the two is different
for first one it's Real
for second it's Real-{-2}

Answer 5

Great! Then is that equal or not?

Answer 6

Yeah they aren't equal:)

Answer 7

Well, but you can proof the equality of these two by mathematical induction, am I right?

Answer 8

No they are not equal.

Answer 9

You can prove them equal by just cancelling the (x+2) in second but their domain is different.
Therefore these two aren't equal

Answer 10

Does anyone have any proof of they are equal or not?

Answer 11

@thomas5267 just by their domain you can prove that they aren't equal. Two functions are equal if their domain as well as range is equal. Here range is equal but domain isn't. So they are not equal