x(x+5)=0, can't divide by zero question

[mickwid]

Hello,

I'm from Hong Kong and I have a question related to your page http://www.purplemath.com/modules/solvquad.htm. x(x+5)=0. You mentioned that "But you can't divide by zero". I would like to clarify if you mean "divide by zero" is conceptually wrong, or divide by zero in this equation can only lead to answer of x=1 and can't lead to x=0 so it is not a good idea.

Another very simple one: x(x+1)=2x, find x. Similarly, x=0 or x=1 like this:

x(x+1)=2x
x^2+x-2x=0
x^2-x=0
x(x-1)=0 <== same as your x(x+5)=0

If we solve like this:

x(x+1)=2x
x(x+1)/=2x/x
x+1=2
x=1

We know that we can never find the answer of x=0 in this way, but is this way "wrong" or "not good"?

Also, if something like xy=3x^2, can we "dividing off the x" to achieve y=3x?
xy/x=3x^2/x
y=3x

This is similar that x can be zero or not and "But you can't divide by zero" apply here or not?

Thank you,
Mickwid.

[little_dragon]

I would like to clarify if you mean "divide by zero" is conceptually wrong, or divide by zero in this equation can only lead to answer of x=1 and can't lead to x=0 so it is not a good idea.

it means U cant do it!
"div by zoer" doesnt mean anything!
its against the rules of math!

[nona.m.nona]

Division by zero is "undefined", meaning that the process has no defined value or definition. The process of dividing by zero is disallowed.