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Math paradox? (again)

#1
First look at those 2 photos.
ibb.co/Lgh335r
ibb.co/QKcjxgc
I am having cross-multiplication in my work now (I already learned it but more as a review).

Sooo.... I decided to ignore my hint and be curious (after all, that's what mathematicians do right?). x=6 was obviously an expected answer.

But wait. x=-3 is also an answer according to my calculations, but if you substitute it into the equation it becomes a...

division by 0. Which makes no sense. And scold me if I'm wrong, but I did the math correctly. I don't understand how correct math gave me 0/0=3. But tell me if you do know :)

Feel free to leave your amazement/scold/something else below :)
#3
and for the 10th one = I think it is x2 -9 = 2x2-9 = 3 and 0 and x-3 = 4 - 3 = 1
Please let me know if I am right.
#4
and for the tenth answer which I said, x2 it means x to the power of 2. I dont know how to put 2 on top on x so I just typed x2
#5
Here's a solution:

In image (1), x cannot be -3. Why? That's because if it were -3, the other side of the equation would also be undefined. But it's not.

In image (2), you multiply both sides by (x + 3). By multiplying, you automatically assume that x is not equal to -3. That's because had it been -3, you would have multiplied both sides of the equation by (-3 + 3) = 0. 2 x 0 = 3 x 0 doesn't mean that 2 = 3.

Had the equation been (x^2 - 9)/(x + 3) = undefined, you would correctly assume that x + 3 = 0, or, x = -3. But since 3 /1 is a rational number, the denominator of the left hand side of the equation can never be 0.

I hope this helps, and if you have any further queries, feel free to mention me in this forum topic itself or DM me.