Question

Why is the other vertical asymptote 0?

Answer 1

Idk if this matters but the question is x+3 / x(x-4)

Answer 2

***Idk if this matters but the question is x+3 / x(x-4)***

yes , it matters; otherwise no one could answer the question
if you have a fraction like for example
\[ \frac{3}{0.001}\]
that simplifies to 3000 (if you multiply top and bottom by 1000, you will get that answer, or if you use a calculator you will get 3000)

if we had an even smaller number, like
\[ \frac{3}{0.000001}\]
that simplifies to 3000000, even bigger.

The point is: dividing by a *tiny* number gives a large number for the answer

now look at
\[ \frac{x+3}{x(x-4)} \]

as x "gets near" zero, as for example: 0.0001 or 0.0000001 or 0.000000001
the answer will get huge. It "asymptotes"

btw, the same thing happens when x gets near 4 because x-4 gets close to zero, and the same thing happens