Simplify the following

**yess** · September 27th 2010, 09:36 PM

1/square root of x^2 -4

**undefined** · September 27th 2010, 09:43 PM

Originally Posted by yess

1/square root of x^2 -4

Do you mean $\frac{1}{\sqrt{x^2}}-4$ or $\frac{1}{\sqrt{x^2-4}}$ ?

I'll assume the first. Note that $\sqrt{x^2}=|x|$ .

**yess** · September 27th 2010, 09:44 PM

sorry! its the second one you wrote =]

**Prove It** · September 27th 2010, 09:45 PM

Multiply it by $\frac{\sqrt{x^2 - 4}}{\sqrt{x^2 - 4}}$ .

**undefined** · September 27th 2010, 09:46 PM

Originally Posted by yess

sorry! its the second one you wrote =]

Well the radicand is not a perfect square.. so perhaps they want you to rationalize the denominator.

**yess** · September 27th 2010, 09:49 PM

so i worked it all out to 1/(x^2 - 4) is that right?

**Prove It** · September 27th 2010, 09:53 PM

No.

What is $\frac{1}{\sqrt{x^2 - 4}}\cdot \frac{\sqrt{x^2 - 4}}{\sqrt{x^2 - 4}}$ ?

**yess** · September 27th 2010, 09:59 PM

Originally Posted by Prove It

No.

What is $\frac{1}{\sqrt{x^2 - 4}}\cdot \frac{\sqrt{x^2 - 4}}{\sqrt{x^2 - 4}}$ ?

(√(x^2 - 4))/(x^2 - 4) ?

**Prove It** · September 27th 2010, 10:05 PM

Correct.

**yess** · September 27th 2010, 10:09 PM

so is that as far as it simplifies then??

**Prove It** · September 27th 2010, 10:12 PM

Originally Posted by yess

so is that as far as it simplifies then??

You can either write it as

$\frac{\sqrt{x^2 - 4}}{x^2 - 4}$ or $\frac{\sqrt{(x-2)(x+2)}}{(x-2)(x+2)}$ , whichever you think is simpler...

**yess** · September 27th 2010, 10:16 PM

Originally Posted by Prove It

You can either write it as

$\frac{\sqrt{x^2 - 4}}{x^2 - 4}$ or $\frac{\sqrt{(x-2)(x+2)}}{(x-2)(x+2)}$ , whichever you think is simpler...

ook so i just leave it the way it is like that? i squared top and bottom to get [(x-2)(x+2)/(x-2)(x+2)(x-2)(x+2)] so 1/(x^2 -4) but thats too far?

**Prove It** · September 27th 2010, 10:19 PM

$\frac{\sqrt{x^2 - 4}}{x^2 - 4} \neq \left(\frac{\sqrt{x^2 - 4}}{x^2 - 4}\right)^2$ .

**mr fantastic** · September 28th 2010, 03:20 AM

Originally Posted by yess

Simplify the following:

1/square root of x^2 -4

Where has the question come from? What is expected by "simplify"? Please give the broader context that the question comes from. There is insufficient information to know what sort of answer is expected.

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