Got me stumped.

[KenyanX]

I'm retaking calculus after many year away from school to prep for a Master's program. I came across a problem that has me stumped. I have the answer, but no matter which way I try to get from point A to point, for the life of me I can't figure out why it is what it is. I did some research and found people asking the same question, but no answers.

Q:

Why does:

x/(sqr(x^2+x) + x) factor to 1/(x sqr(1 + (1/x)) + 1)

Things I understand about the problem.

1. I understand dividing the numerator and denominator by x to factor out an x
2. I realize this is Algebra and not calculus The equation is the result of the conjugate multiplication of a limit.

I'm getting lost as to why sqr(x^2 + x) becomes sqr (1 + 1/x) though. I know there probably is an easy rule I'm forgetting.

Please help!

 

[lookagain]

It doesn't.

\(\displaystyle \sqrt{x^2 + x} = \)

\(\displaystyle \sqrt{x^2\left(1 + \dfrac{1}{x}\right)} = \)

\(\displaystyle \sqrt{x^2} * \sqrt{1 + \dfrac{1}{x}} = \)

\(\displaystyle |x| \sqrt{1 + \dfrac{1}{x}}.\) Do not forget the absolute value bars here
and elsewhere in the steps.

...

 

[KenyanX]

First, Thanks so much. the issue I was having a issue on was factoring the square root and you guys explained it perfect.

The equation I was trying to solve. (wish I knew how to type the fancy graphical math equations that you guys did on the forum - so you'll need to bare with my calculator notation)

It was the limit as x--> infinity of

(x^2)/(sqr(x^ + x) +1)

I knew I needed to factor out an x by dividing the numerator and denominator by x, but the square root was stumping me.

 

[HallsofIvy]

The fancy rendering uses a LaTex interpreter, which is part of the site. Unfortunately, the site does not have a tutorial on how to use LaTex. If you use the site OFTEN ENOUGH, you may want to try to learn LaTex. One slow but easy way to do so is to hit reply with quote on some post that has LaTex renderings. You will then see the code actually used. So if you go and hit reply with quote on my original post you will see the code I used in that post. The other way is to ask, presumably under Odds and Ends, about to how to do something in LaTex.

"Physics Forums" has a nice introduction to LaTex (not really a tutorial) at
http://www.physicsforums.com/showthread.php?t=8997