Why can't I simplify 3x = x^2? Is it because the result will not be equal to the original expression?

Question

juanperez · Answer

If you simplify you get x=3, which is right, but you will miss the other solution, x=0

anonymous · Answer

Why does the same operation work when you divide out exponentials? Because then there is only one solution to be found?

anonymous · Answer

that is, natural exponentials

juanperez · Answer

What happens is that when you simplify you divide by x, which is only valid if x is not 0

anonymous · Answer

you can find the solution like this (but I don't know if this would be considered "simplifying"):

3x = x^2
x^2 - 3x = 0
x(x - 3) = 0

Then you don't lose any solutions... x = 0 or x = 3

anonymous · Answer

The question says there is an important reason why I can't just go and simplify it

anonymous · Answer

Then @JuanPerez's reason is exactly right!