Question

2х-1 2х+1 4
___ - ___ + ___
2х+1 2х-1 1-4х^2

Answer 1

Ответ:

$\displaystyle -\frac{4}{2x-1}$

Объяснение:

$\displaystyle \frac{2x-1}{2x+1}-\frac{2x+1}{2x-1}+\frac{4}{1-4x^2}=\\\\\\\frac{(2x-1)^2}{(2x+1)(2x-1)}-\frac{(2x+1)^2}{(2x+1)(2x-1)}-\frac{4}{4x^2-1}=\\\\\\\frac{(2x-1)^2-(2x+1)^2}{(2x+1)(2x-1)}-\frac{4}{(2x+1)(2x-1)}=\\\\\\\frac{4x^2-4x+1-(4x^2+4x+1)-4}{(2x+1)(2x-1)}=\\\\\\\frac{4x^2-4x+1-4x^2-4x-1-4}{(2x+1)(2x-1)}=\\\\\\\frac{-8x-4}{(2x+1)(2x-1)}=\frac{-4(2x+1)}{(2x+1)(2x-1)}=-\frac{4}{2x-1}$