Question 1122263
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There are a couple of ways to get there.  The straight-up way is to simply do polynomial long division on the original rational expression:


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            6 
      ________
x + 4 )6x -  1
       6x + 24  {remember, change the sign and add}
       _______
          - 25
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So *[tex \Large x\ +\ 4] goes into *[tex \Large 6x\ -\ 1] 6 times with a remainder of -25.  Or, as answer A puts it:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6\ -\ \(\frac{25}{x\ +\ 4}\)]


Or you could just get clever and notice that -1 can be written as 24 - 25:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{6x\ +\ 24\ -\ 25}{x\ +\ 4}\ =\ \frac{6x\ +\ 24}{x\ +\ 4}\ -\ \frac{25}{x\ +\ 4}\ =\ \frac{6(x\ +\ 4)}{x\ +\ 4}\ -\ \frac{25}{x\ +\ 4}\ =\ 6\ -\ \frac{25}{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}}
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