Dividing by zero

[Simsim]

So: x*(x+1)/x = (x+1), then when x approaches zero (x+1) approaches 1

That's totally wrong.

x*(x+1)/x approaches 1, if and only if x is NOT zero. At x=0, that algebraic fraction is infinite.

Sorry, have you read what you quoted for me??

I didn't say that x can be 0

Again:

So: x*(x+1)/x = (x+1), then when x approaches zero (x+1) approaches 1

And your expression is wrong. :

"" x*(x+1)/x approaches 1, if and only if x is NOT zero. At x=0, that algebraic fraction is infinite. ""

Wrong ! That means that whatever the value of x is, the value of the fraction approaches 1 as long as x doesn't equal zero ! That's obviously wrong !

And when x=0 the algebraic fraction will not be infinite as you said. It will be "undefined".