[tex]x\neq0\ \wedge\ x-3\neq0\ \wedge\ x+3\neq0\\\\x\neq0\ \wedge\ x\neq3\ \wedge\ x\neq - 3\\[/tex]
[tex](x - \frac{9}{x} ) \times ( \frac{1}{x - 3} - \frac{1}{x + 3} ) \div (1 + \frac{1}{x}) = \\ \\ \frac{ {x}^{2} - 9}{x} \times \frac{x + 3 - (x - 3)}{(x - 3)(x + 3)} \div \frac{x + 1}{x} = \\ \\ \frac{(x + 3)(x - 3)}{x} \times \frac{6}{(x - 3)(x + 3)} \times \frac{x}{x + 1} = \\ \\ \frac{6}{x} \times \frac{x}{x + 1} = \\ \\ \frac{6}{x + 1} \\ [/tex]
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[tex]x\neq0\ \wedge\ x-3\neq0\ \wedge\ x+3\neq0\\\\x\neq0\ \wedge\ x\neq3\ \wedge\ x\neq - 3\\[/tex]
[tex](x - \frac{9}{x} ) \times ( \frac{1}{x - 3} - \frac{1}{x + 3} ) \div (1 + \frac{1}{x}) = \\ \\ \frac{ {x}^{2} - 9}{x} \times \frac{x + 3 - (x - 3)}{(x - 3)(x + 3)} \div \frac{x + 1}{x} = \\ \\ \frac{(x + 3)(x - 3)}{x} \times \frac{6}{(x - 3)(x + 3)} \times \frac{x}{x + 1} = \\ \\ \frac{6}{x} \times \frac{x}{x + 1} = \\ \\ \frac{6}{x + 1} \\ [/tex]