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[tex]\frac{9a}{(3-a)^2}-1:(\frac{a}{a-3}+\frac{12a^2-9a}{27-a^3}+\frac{9}{a^2+3a+9})[/tex]

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laymlaym2

$\frac{9a}{(3-a)^2}-1:(\frac{a}{a-3}+\frac{12a^2-9a}{(3)^3-a^3}+\frac{9}{a^2+3a+9})=\\=\frac{9a}{(3-a)^2}-1:(\frac{a}{a-3}+\frac{12a^2-9a}{(3-a)(9+3a+a^2)}+\frac{9}{a^2+3a+9})=\\=\frac{9a}{(3-a)^2}-1:(\frac{a}{a-3}-\frac{12a^2-9a}{(a-3)(9+3a+a^2)}+\frac{9}{a^2+3a+9})=\\=\frac{9a}{(3-a)^2}-1:(\frac{a^3+3a^2+9a-12a^2+9a+9a-27}{(a-3)(a^2+3a+9)})=\\=\frac{9a}{(3-a)^2}-1:(\frac{a^3-9a^2+27a-27}{(a-3)(a^2+3a+9)})=\\=\frac{9a}{(3-a)^2}-\frac{(a-3)(a^2+3a+9)}{(a^3-3^3)+(-9a^2+27a)}=$

$=\frac{9a}{(a-3)^2}-\frac{(a-3)(a^2+3a+9)}{(a-3)(a^2+3a+9)-9a(a-3)}=\\=\frac{9a}{(a-3)^2}-\frac{(a-3)(a^2+3a+9)}{(a-3)(a^2+3a+9-9a)}=\\=\frac{9a}{(a-3)^2}-\frac{a^2+3a+9}{a^2-6a+9}=\\=\frac{9a}{(a-3)^2}-\frac{a^3+3a+9}{(a-3)^2}=\frac{9a-a^2-3a-9}{(a-3)^2}=\\=\frac{-(a^2-6a+9)}{(a-3)^2}=-\frac{(a-3)^2}{(a-3)^2}=-1$

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