Question

((x-2/3x+6)+(1/x^2-4)+(x-6/6-3x))*(9x^2-36)/32

Answer 1

Решение:

$\Big (\dfrac{x-2}{3x+6} + \dfrac{1}{x^2-4} +\dfrac{x-6}{6 -3x}} \Big )\cdot \dfrac{9x^2 - 36}{32} = \\ \\=\Big (\dfrac{x-2}{3(x+2)} + \dfrac{1}{x^2-4} -\dfrac{x-6}{3(x - 2)}} \Big )\cdot \dfrac{9x^2 - 36}{32} =\\ \\=\Big (\dfrac{(x-2)(x-2)}{3(x^2-4)} + \dfrac{3}{3(x^2-4)} -\dfrac{(x-6)(x+2)}{3(x^2 - 4)}} \Big )\cdot \dfrac{9x^2 - 36}{32} =\\ \\=\Big (\dfrac{x^2 - 4x + 4 +3 - x^2+4x+12}{3(x^2-4)} \Big )\cdot \dfrac{9(x^2 - 4)}{32} =\\ \\=\dfrac{19}{3(x^2 - 4)} \cdot \dfrac{9(x^2 - 4)}{32} =$

$= \dfrac{57}{32} = 1\dfrac{25}{32}$