Question 1122265
<font face="Times New Roman" size="+2">


You can't get to where you want to be from where you are starting.  I suspect, however, that you have a sign error in the original expression:


You wrote:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\(1\ -\ \sqrt{x\ +\ 4}\)\(1\ -\ \sqrt{x\ +\ 4}\)}{(x\ +\ 3)\(1\ +\ \sqrt{x\ +\ 4}\)}]


And I believe you really meant:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\(1\ -\ \sqrt{x\ +\ 4}\)\(1\ +\ \sqrt{x\ +\ 4}\)}{(x\ +\ 3)\(1\ +\ \sqrt{x\ +\ 4}\)}]


In fact, what I think is going on is that you actually began with:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\(1\ -\ \sqrt{x\ +\ 4}\)}{(x\ +\ 3)}]


And your goal was to rationalize the numerator.


So, presuming that you are working with:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{\(1\ -\ \sqrt{x\ +\ 4}\)\(1\ +\ \sqrt{x\ +\ 4}\)}{(x\ +\ 3)\(1\ +\ \sqrt{x\ +\ 4}\)}]


Note that the two factors in the numerator are a conjugate pair, i.e., of the form *[tex \Large (a\ -\ b)(a\ +\ b)] which you should recognize as the factorization of the difference of two squares.  Hence, your numerator reduces to:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1\ -\ (x\ +\ 4)}{(x\ +\ 3)\(1\ +\ sqrt{x\ +\ 4}\)}\ =\ \frac{-(x\ +\ 3)}{(x\ +\ 3)\(1\ +\ sqrt{x\ +\ 4}\)}\ =\ -\frac{1}{\(1\ +\ sqrt{x\ +\ 4}\)}]

								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
</font>