[tex] \cfrac{x^2-81}{x^2\underline{-6x}-27} \cdot \cfrac{x+3}{x}= \cfrac{(x-9)(x+9)}{x^2\underline{+3x-9x}-27} \cdot \cfrac{x+3}{x}= \\ \\ \\ \\=\cfrac{(x-9)(x+9)}{x(x+3)-9(x+3)} \cdot \cfrac{x+3}{x}=\cfrac{(x-9)(x+9)}{(x+3)(x-9)} \cdot \cfrac{x+3}{x}= \boxed{\frac{x+9}{x} } [/tex]
