Question

Решите пожалуйста: (x+3/x^2-3x+12/9-x^2)*3x/x-3

Answer 1

Решение во вложении.

Answer 2

$( frac{x + 3}{ {x}^{2} - 3x } + frac{12}{9 - {x}^{2} } )cdot frac{3x}{x-3} = frac{3}{x + 3}$
$1) : frac{x + 3}{ {x}^{2} - 3x} + frac{12}{9 - {x}^{2} } = frac{x + 3}{x(x - 3)} - frac{12}{ {x}^{2} - 9} = \ = frac{x + 3}{x(x - 3)} - frac{12}{ {x}^{2} - {3}^{2} } = frac{x + 3}{x(x - 3)} - frac{12}{(x - 3)(x + 3)} = \ = frac{(x + 3)^2-12x}{x(x - 3)(x + 3)} = frac{ {x}^{2} + 2cdot xcdot3 + 3^{2} - 12x}{x(x - 3)(x + 3)} =$
$= frac{ {x}^{2} + 6x + {3}^{2} - 12x }{x(x - 3)(x + 3)} = frac{ {x}^{2} - 6x + {3}^{2} }{x(x - 3)(x + 3)} = \ = frac{ {x}^{2} - 2cdot xcdot3 + 3^{2}}{x(x - 3)(x + 3)} = frac{ {(x - 3)}^{2} }{x(x - 3)(x + 3)} = frac{ x - 3}{x(x + 3)}$
$2) : frac{ x - 3}{x(x + 3)} cdot frac{3x}{x - 3} = frac{3}{x + 3}$
Ответ:
$frac{3}{x +3}$