Question

•Упростите выражение:
(3/9-Xквадрат + 1/X-3) : X/Xквадрат-6X+9

Answer 1

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

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