Answer:
See Explanation
Step-by-step explanation:
Given
[tex]3x^2 = 6x[/tex]
Required
Why dividing by [tex]3x[/tex] is not reliable
The reason is that, the given expression is a quadratic equation and as such, it will most likely have two solutions.
So, when the expression is divided by [tex]3x[/tex], the solution will be [tex]x = 2[/tex], leaving out the other possible solution.
The right way is:
[tex]3x^2 = 6x[/tex]
Subtract 6x from both sides
[tex]3x^2 - 6x = 6x - 6x[/tex]
[tex]3x^2 - 6x = 0[/tex]
Factorize
[tex]3x(x - 2) = 0[/tex]
Split
[tex]3x = 0\ or\ x - 2 = 0[/tex]
Solve for x in both cases:
[tex]x = 0\ or\ x = 2[/tex]
