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

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

can someone double check this? Thanks

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

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

3. how did you get x-4?

thanks

4. ooo i got it! thanks!

5. Code:
         x - 4
..............................
x+4 |  x^2
x^2 + 4x
..................
- 4x
- 4x - 16
..............
16

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