# Simplifying

• Oct 11th 2013, 06:45 AM
Paze
Simplifying
Wait, rephrasing this question
• Oct 11th 2013, 06:56 AM
topsquark
Re: Simplifying
Quote:

Originally Posted by Paze
I have ran across a calculus problem where a maxima/minima was defined but in reality it wasn't.

The reason was that I needed to simplify my equation.

My question is two-fold:

How do I simplify x^2-2x+26?

Why is it so important to simplify equations? How does it change the outcome without changing the content? Thanks!

The original differentiated equation was:

$\displaystyle \frac{x^2-2x+26}{(x-1)^2}=0$

Unless you want to factor the numerator over the reals, this is as simplified as it's going to get.
$\displaystyle \frac{x^2-2x+26}{(x-1)^2} = \frac{(x - (1 + 5i))(x - (1 - 5i))}{(x - 1)^2}$

I don't see how this helps, so I'd leave it in the form you put it in.

In general you want to simplify the expression as much as you can. This is either for the sake of clarity or perhaps because you are going to use the expression later and you want to make it as "simple" as possible.

-Dan
• Oct 11th 2013, 07:06 AM
Paze
Re: Simplifying
Quote:

Originally Posted by topsquark
Unless you want to factor the numerator over the reals, this is as simplified as it's going to get.
$\displaystyle \frac{x^2-2x+26}{(x-1)^2} = \frac{(x - (1 + 5i))(x - (1 - 5i))}{(x - 1)^2}$

I don't see how this helps, so I'd leave it in the form you put it in.

In general you want to simplify the expression as much as you can. This is either for the sake of clarity or perhaps because you are going to use the expression later and you want to make it as "simple" as possible.

-Dan

Thanks, Dan. I made a mistake in this thread which I had been dealing with for an hour but of course noticed as soon as I made a thread!

However, my original question is still valid and has been clarified at: http://mathhelpforum.com/algebra/222...tml#post800276
• Oct 11th 2013, 07:17 AM
votan
Re: Simplifying
Quote:

Originally Posted by topsquark
Unless you want to factor the numerator over the reals, this is as simplified as it's going to get.
$\displaystyle \frac{x^2-2x+26}{(x-1)^2} = \frac{(x - (1 + 5i))(x - (1 - 5i))}{(x - 1)^2}$

I don't see how this helps, so I'd leave it in the form you put it in.

In general you want to simplify the expression as much as you can. This is either for the sake of clarity or perhaps because you are going to use the expression later and you want to make it as "simple" as possible.

-Dan

I would define z = 1 + 5i, then the fraction becomes (x - z)(x - z*)/(x - 1)^2. Perhaps this would make the OP happier