Question

Решите уровнение
6/1-2х+9/2х+1=12х^2-15/4х^2-1

Answer 1

$frac{6}{1-2x} + frac{9}{2x+1} = frac{12x^{2}-15}{4x^{2}-1}$
$frac{9}{2x+1} - frac{6}{2x-1} - frac{12x^{2}-15}{(2x-1)(2x+1)}=0$
$left { {{9(2x-1)-6(2x+1)-(12x^{2}-15) = 0} atop {2x-1 neq 0; 2x+1 neq 0}} right.$
$left { {18x-9-12x-6-12x^{2}+15 = 0} atop {x neq pm frac{1}{2}} right.$
$left { {-12x^{2}+6x = 0} atop {x neq pm frac{1}{2}} right.$
$left { {2x^{2}-x = 0} atop {x neq pm frac{1}{2}} right.$
$left { {x(2x-1) = 0} atop {x neq pm frac{1}{2}} right.$
$left { {x = 0; x = frac{1}{2}} atop {x neq pm frac{1}{2}} right.$
$x = 0$