Question

•выражение: (3/9-xквадрат + 1/x-3) : x/xквадрат-6x+9

Answer 1

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

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