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Answer 1

$\frac{ {x}^{2} }{ {x}^{2} + 5x + 6} - \frac{4}{x + 2} + \frac{9}{x + 3} = \\ \frac{ {x}^{2} }{(x + 2)(x + 3)} - \frac{4}{x + 2} + \frac{9}{x + 3} = \\ \frac{ {x}^{2} }{(x + 2)(x + 3)} - \frac{4(x + 3)}{(x + 2)(x + 3)} + \frac{9(x + 2)}{( x + 2)(x + 3)} = \\ \frac{ {x}^{2} - 4(x + 3) + 9(x + 2)}{(x + 2)(x + 3)} = \\ \frac{ {x}^{2} - 4x - 12 + 9x + 18 }{ {x}^{2} + 5x + 6} = \\ \frac{ {x}^{2} + 5x + 6}{ {x}^{2} + 5x + 6 } = 1$