Long division! intregration of rational functions by partial fractions

**softballchick** · August 4th 2010, 06:09 PM

$Long division! intregration of rational functions by partial fractions-long-division.jpg$

can someone double check this? Thanks

edit: for the second row and 3rd row, I meant to write X instead of r

**skeeter** · August 4th 2010, 06:21 PM

$\displaystyle \frac{x^2}{x+4} = x - 4 + \frac{16}{x+4}$

**softballchick** · August 4th 2010, 06:32 PM

how did you get x-4?

thanks

**softballchick** · August 4th 2010, 06:36 PM

ooo i got it! thanks!

**skeeter** · August 4th 2010, 06:38 PM

Code:

         x - 4
..............................
x+4 |  x^2
       x^2 + 4x
        ..................
           - 4x
           - 4x - 16
              ..............
                  16

**HallsofIvy** · August 5th 2010, 03:30 AM

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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