Question

Va rog frumos .....!!!!!!

Answer 1

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Answer 2

$\frac{ {x}^{2} - 81 }{ {x}^{3} + {18x}^{2} + 81x } = \frac{ {x}^{2} - {3}^{4} }{ {x}^{3} + 2 \times {3}^{2} \times {x}^{2} + {3}^{4} \times x } = \frac{ {x}^{2} - ( { {3}^{2}) }^{2} }{x( \frac{ {x}^{3} }{x} + \frac{2 \times {3}^{2} \times {x}^{2} }{x} + \frac{ {3}^{4} \times x }{x}) } = \frac{( {x - 3}^{2})(x + {3}^{2}) }{x( {x}^{3 - 1} + 2 \times {3}^{2} \times {x}^{2 - 1} + {3}^{4}) } = \frac{(x - 9)(x + 9)}{x( {x}^{2} + 2 \times 9x + 81) } = \frac{(x - 9)(x + 9)}{x( {x}^{2} + 18x + 81) } = \frac{(x - 9)(x + 9)}{x( {x}^{2} + 2x \times 9 + {9}^{2}) } = \frac{(x - 9)(x + 9)}{x(( {x + 9})^{2}) } = \frac{x - 9}{x(x + 9) ^{2 - 1} } = \frac{x - 9}{x(x + 9)}$