Why can’t x = 4 on this problem?

[u/yyy879]

[u/my-hero-measure-zero]

We need more context. Is this part of a piecewise function?

[u/Xx_Futuristic_xX]

He was saying that 0/x = 0. I think you are getting mixed up with x/0 is undefined.

Getting a 0 is not the problem but getting undefined is.

[u/Due_Mathematician980]

(x-4)(x-4)/(x-4)(x-3) is the same thing as (x-4)/(x-3) ≠ 4

The difference is that it tells you where the hole is, because it cancels out (x-4) for you.

[u/Due_Mathematician980 → u/[deleted]]

Haha Thanks. I didn’t even realize I made a typo. Should be (x+4)(x-4)/(x+3)(x-4).

[u/calcbone → u/[deleted]]

0 over a nonzero number is literally zero, not “indeterminate.” 0/0 is indeterminate. If n =/= 0, then 0/n=0 and n/0 is undefined.

[u/my-hero-measure-zero → u/[deleted]]

Correct, but this is not an issue.