Can't find mistake in logic?

Question

Here's the question:
assume x^2+3x+2=0
this factors to
(x+2)(x+1)=0

Now divide both sides by
(x+2)(X+1),
and you get

((x+2)(X+1))/((x+2)(X+1))=0/((x+2)(X+1))
For the left side, you get (x+2)(X+1) over itself, which is one, while for the right, since you are dividing 0, you get zero. This leaves you with:
1=0, which is obviously not right, where is the mistake in this problem?

Answer 1

Since (x+2)(x+1)=0, you can't divide by (x+1)(x+2), because you'd be dividing by zero.

Answer 2

You have already pointed out your mistake in this question.
You stated,

(x + 2)(x + 1) = 0

Now, if you divide both sides by (x + 2)(x + 1), this means you are actually dividing the entire equation by 0. Now, anything that has a denominator of 0 is undefined and it cannot be done.

Answer 3

The solutions are x=1 and x=2 either of which makes the right side=0. You have assumed that o/o=1but 0/0=0

Answer 4

The mistake is that for your polynomial to equal zero, then x must equal -2 or -1, in which case it already is zero. So what you're really doing is dividing zero by zero, which as you'll see in calculus has infinite solutions.

Answer 5

(x+2)(x+1) is already equal to 0
you cannot again divide it by by (x+2)(X+1) cause it would be like ur dividing by 0 again

Answer 6

It's just the same as if you said:

a = 0

Divide both sides by a:
a/a = 0
1 = 0

As others have noted, you are dividing by zero and that is not allowed!

Answer 7

Dividing by zero is not a defined operation, regardless of the numerator.