Simplifying to get the correct answer

• Oct 11th 2013, 07:05 AM
Paze
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:

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

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:

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

How come this is so important? How does it change the whole ordeal to simplify without changing the content?
Thanks!
• Oct 11th 2013, 07:14 AM
Well, plug in $x=1$ into your first equation. You'll get $\frac{0}{0}$. You can't divide by 0, which means that the function never equals 0. Simplifying it makes it easier to see.