Question

упростить выражение (х²+9/х²-6х+9. +. х-3/3-х) : 9/х²-9​

Answer 1

Объяснение:

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