Simplifying to get the correct answer

Hi MHF.

I have noticed that sometimes, you run into problems where you will get a wrong answer unless you simplify.

For example:

$\displaystyle \frac{3x-3}{x^2-1}=0$

If I simply multiply both sides by x^2-1, I get 3x-3=0 or 3x=3 or x=1.

However, the true answer is that there are no roots.

That can be obtained by simplifying:

$\displaystyle \frac{3(x-1)}{(x-1)(x+1)}=\frac{3}{x+1}=false$

How come this is so important? How does it change the whole ordeal to simplify without changing the content?

Thanks!

Re: Simplifying to get the correct answer

Well, plug in $\displaystyle x=1$ into your first equation. You'll get $\displaystyle \frac{0}{0}$. You can't divide by 0, which means that the function never equals 0. Simplifying it makes it easier to see.

I recommend that whenever you find a solution, plug it into an equation to verify.