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Math Help - Long division! intregration of rational functions by partial fractions

  1. #1
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    Long division! intregration of rational functions by partial fractions

    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
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  2. #2
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    \displaystyle \frac{x^2}{x+4} = x - 4 + \frac{16}{x+4}
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  3. #3
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    how did you get x-4?

    thanks
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    ooo i got it! thanks!
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  5. #5
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    Code:
             x - 4
    ..............................
    x+4 |  x^2
           x^2 + 4x
            ..................
               - 4x
               - 4x - 16
                  ..............
                      16
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  6. #6
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    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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