lim x-> 9 x²-8x-9 / √x-3

[tex]= \frac{ {x}^{2} - 8x - 9 }{ \sqrt{x} - 3 } \\ = \frac{ (x - 9)(x + 1) }{ \sqrt{x} - 3 } \times \frac{( \sqrt{x} + 3) }{( \sqrt{x} + 3)} \\ = \frac{ (x - 9)(x + 1)( \sqrt{x} + 3) }{ (x - 9) } \\ = (x + 1)( \sqrt{x} + 3) \\ = 3x + x \sqrt{x} + x + 3 \\ = 3(9) + 9 \sqrt{9} + \sqrt{9} + 3 \\= 27 + 27 + 3 + 3 \\ = 60[/tex]