Question

50 баллов
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Answer 1

$2)\ \ (a^{-2})^{10}:a^{-27}=a^{-20}:a^{-27}=a^7\\\\4)\ \ \dfrac{x-1}{2x^2-5x+2}\ \ \to \ \ \ 2x^2-5x+2\ne 0\ \ ,\ \ x_1\ne 0,5\ ,\ \ x_2\ne 2$

$5)\ \ \dfrac{3}{2a-3}-\dfrac{8a^3-18a}{4a^2+9}\cdot \Big(\dfrac{2a}{4a^2-12a+9}-\dfrac{3}{4a^2-9}\Big)=\\\\\\=\dfrac{3}{2a-3}-\dfrac{2a\, (4a^2-9)}{4a^2+9}\cdot \Big(\dfrac{2a}{(2a-3)^2}-\dfrac{3}{(2a-3)(2a+3)}\Big)=\\\\\\=\dfrac{3}{2a-3}-\dfrac{2a\, (2a-3)(2a+3)}{4a^2+9}\cdot \dfrac{2a(2a+3)-3(2a-3)}{(2a-3)^2(2a+3)}=\\\\\\=\dfrac{3}{2a-3}-\dfrac{2a}{4a^2+9}\cdot \dfrac{4a^2+9}{2a-3}=\dfrac{3}{2a-3}-\dfrac{2a}{2a-3}=\dfrac{3-2a}{2a-3}=\dfrac{-(2a-3)}{2a-3}=-1\\\\\\-1=-1$