Question

Выражение: x-4/x^3-x : (x-1/2x^2+3x+1 - 1/x^2-1)

Answer 1

$\frac{x-4}{ x^{3} -x} : (\frac{x-1}{2 x^{2} +3x+1}- \frac{1}{ x^{2} -1})= \frac{x-4}{x(x-1)(x+1)}:( \frac{x-1}{(x+1)(2x+1)}- \frac{1}{(x-1)(x+1)})= \\ \\ \frac{x-4}{x(x-1)(x+1)}:( \frac{(x-1)(x-1)-2x-1}{(x+1)(x-1)(2x+1)})= \frac{x-4}{x(x-1)(x+1)}* \frac{(x+1)(x-1)(2x+1)}{ x^{2} -2x+1-2x-1}= \\ \\ \frac{(x-4)(2x+1)}{x( x^{2} -4 x )}= \frac{(x-4)(2x+1)}{ x^{2} (x-4)}= \frac{2x+1}{ x^{2} }$