[tex] \frac{3 + \frac{x - 3}{9 - {x}^{2} } }{3 -\frac{4}{x + 3} } \\ = \frac{ \frac{3(9 - {x}^{2} ) + x - 3}{9 - {x}^{2} } }{ \frac{3(x + 3) - 4}{x + 3} } \\ = \frac{27 - 3 {x}^{2} + x - 3}{9 - {x}^{2} } \times \frac{x + 3}{3x + 12 - 4} \\ = \frac{ - 3 {x}^{2} + x + 24 }{ - (x - 3)(x + 3)} \times \frac{x + 3}{3x + 8} \\ = \frac{ - (3x + 8)(x - 3)}{ - (x - 3)} \times \frac{1}{3x + 8} \\ = \frac{ - (x - 3)}{ - (x - 3)} \\ = 1[/tex]
Hope this helps. - M
