Question: For x>0, simplify the following:

$\displaystyle

\sqrt{x^4-4x^2}/x

$

Hint: If x<0, what is :

$\displaystyle

\sqrt{x^2}

$

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- May 20th 2009, 11:53 PMmvhoSimplify and Rationalize
Question: For x>0, simplify the following:

$\displaystyle

\sqrt{x^4-4x^2}/x

$

Hint: If x<0, what is :

$\displaystyle

\sqrt{x^2}

$ - May 21st 2009, 01:46 AMyeongil
No, rationalizing the denominator doesn't mean multiplying by a conjugate. You just multiply the numerator & denominator by the denominator itself:

$\displaystyle \frac{m-4}{\sqrt{m-4}}$

$\displaystyle \frac{m-4}{\sqrt{m-4}}*\frac{\sqrt{m-4}}{\sqrt{m-4}}$

$\displaystyle \frac{(m-4)\sqrt{m-4}}{m-4}$

$\displaystyle \sqrt{m-4}$

I didn't do #1 or #2 because I couldn't figure out what your problems were. Can you use the math tags or put in some parentheses?

01 - May 21st 2009, 02:29 AMSingaporean
Er i am assuming that the square root applies to only $\displaystyle x^4$

1.$\displaystyle \frac{\sqrt (x^4)-(4x^2)}{x}$

$\displaystyle \frac{(x^2)-(4x^2)}{x}$

$\displaystyle x-(4x)$

$\displaystyle -3x$

lol think so - May 21st 2009, 01:04 PMmvho
Hmm... The square root for question #3, ends at the m. Ill have to find out how to use math tags.

Any links to learn how to use math tags? I need that sq. root symbol! - May 21st 2009, 02:07 PMyeongil
Please do! So you mean

$\displaystyle \frac{m - 4}{\sqrt{m} - 4}$?

Then yes, you would multiply by the conjugate:

$\displaystyle \frac{m - 4}{\sqrt{m} - 4} * \frac{\sqrt{m} + 4}{\sqrt{m} + 4}$

$\displaystyle \frac{(m - 4)(\sqrt{m} + 4)}{(\sqrt{m})^{2} - 4^{2}}$

$\displaystyle \frac{(m - 4)(\sqrt{m} + 4)}{m - 16}$

Dunno if it's necessary to FOIL the numerator. There's nothing else to simplify that I can see.

01 - May 21st 2009, 02:28 PMmvho
yeongil: Thats right. That is what I got too. How do yo use these math tags though? Is there a FAQ somewhere?

Quote:

Er i am assuming that the square root applies to only http://www.mathhelpforum.com/math-he...1fb8a76a-1.gif

The square root applies to the entire numerator. I need to learn about these math tags!! - May 22nd 2009, 02:38 AMSingaporean
http://www.mathhelpforum.com/math-he...-tutorial.html

the file attached there should explain everything. - May 22nd 2009, 01:30 PMmvho
Thanks for the link! I have revised my question now, so it Should be much clearer.

I am unclear what the hint is implying, does anyone have a clue?

Here is my answer:

$\displaystyle

-\sqrt{x^2-4}

$

I know I can simplify further (difference of squares) but this looks neater and I m done fooling around with latex for 1 day