Long division! intregration of rational functions by partial fractions

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August 4th 2010, 06:09 PM
softballchick

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Long division! intregration of rational functions by partial fractions

Attachment 18443

can someone double check this? Thanks

edit: for the second row and 3rd row, I meant to write X instead of r
August 4th 2010, 06:21 PM
skeeter

$\displaystyle \frac{x^2}{x+4} = x - 4 + \frac{16}{x+4}$
August 4th 2010, 06:32 PM
softballchick

how did you get x-4?

thanks
August 4th 2010, 06:36 PM
softballchick

ooo i got it! thanks!
August 4th 2010, 06:38 PM
skeeter

Code:

x - 4 .............................. x+4 | x^2 x^2 + 4x .................. - 4x - 4x - 16 .............. 16
August 5th 2010, 03:30 AM
HallsofIvy

Or $\frac{x^2}{x+ 4}= \frac{x^2- 16+ 16}{x+ 4}= \frac{x^2- 16}{x+ 4}+ \frac{16}{x+ 4}$ $= \frac{(x- 4)(x+ 4)}{x- 4}+ \frac{16}{x+ 4}= x- 4+ \frac{16}{x+ 4}$ .

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