Question

$frac{2x+1}{2x-1} + frac{8}{1-4 x^{2} }= frac{3(2x-1)}{7(2x+1)}$
ПОМОГИИТЕ

Answer 1

$frac{2x+1}{2x-1}- frac{8}{(2x-1)(2x+1)}- frac{3(2x-1)}{7(2x+1)}=0 \ \ x neq 0.5 \ x neq -0.5$

Общий знаменатель:
7(2х-1)(2х+1)

$7(2x+1)^2-8*7-3(2x-1)^2=0 \ 7(4x^2+4x+1)-56-3(4x^2-4x+1)=0 \ 28x^2+28x+7-56-12x^2+12x-3=0 \ 16x^2+40x-52=0 \ 4x^2+10x-13=0$
$D=100+208=308 \ x_{1}= frac{-10- sqrt{308} }{8}= frac{-10-2 sqrt{77} }{8}= frac{-5- sqrt{77} }{4} \ x_{2}= frac{-5+ sqrt{77} }{4}$