Question

Решите уравнение
$frac{3}{x+2} - frac{2x-1}{x+1} = frac{2x+2}{ x^{2} +3x+2}$

Answer 1

$frac{3}{x+2} - frac{2x-1}{x+1} = frac{2x+2}{ x^{2} +3x+2}$
$3(x+1)-(x+2)(2x-1)=2x+2$
$5-2 x^{2} =2x+2$
$-2 x^{2} -2x+3=0$
$x^{2} +x- frac{3}{2} =0$
$x^{2} +x= frac{3}{2}$
$x^{2} +x+ frac{1}{4} = frac{7}{4}$
$(x+ frac{1}{2} )^2= frac{7}{4}$
$x+ frac{1}{2} = frac{ sqrt{7} }{2}$ или
$x+ frac{1}{2} =- frac{ sqrt{7} }{2}$
$x= - frac{1}{2} - frac{ sqrt{7} }{2}$