[tex] \frac{x-5}{ x^{3} +27} + \frac{2}{ x^{2} -9} = \frac{x-5}{ x^{3}+27 } + \frac{2}{(x+3)(x-3)} \\ \\ long-division.. \\ (x^{3} +27)/(x+3) = x^{2} -3x+9 \\ \\ \frac{x-5}{(x+3)( x^{2} -3x+9)} + \frac{2}{(x+3)(x-3)} \\ \\ \frac{x-5}{(x+3)( x^{2} -3x+9)}* \frac{x-3}{x-3} + \frac{2}{(x+3)(x-3)} * \frac{x^{2} -3x+9}{ x^{2} -3x+9} = \frac{(x-5)(x-3)+2( x^{2} -3x+9)}{(x+3)(x-3)( x^{2} -3x+9)} [/tex]
[tex]\frac{(x-5)(x-3)+2( x^{2} -3x+9)}{(x+3)(x-3)( x^{2} -3x+9)} = \frac{ x^{2} -8x+15+2x^{2} -6x+18}{(x+3)(x-3)( x^{2} -3x+9)} \\ \\ \frac{ 3x^{2} -14x+33}{(x+3)(x-3)( x^{2} -3x+9)}[/tex]
