Решите уравнение: 3х 2х 8 ------------- - ------------ = --- х^2-4х+1 х^2+х+1 3

$\frac{3x}{ x^{2} - 4x + 1} - \frac{2x}{ x^{2} +x+1} = \frac{8}{3}$
разделим числитель и знаменатель каждой дроби на х:

$\frac{3}{x-4+ \frac{1}{x} } - \frac{2}{x+1+ \frac{1}{x} } = \frac{8}{3}$
$x+ \frac{1}{x} =t$
3/(t - 4) - 2/(t + 1) = 8/3
9(t + 1) - 6(t - 4) = 8(t - 4)(t + 1)
9t + 9 - 6t + 24 - 8t² + 24t + 32 = 0
8t² - 27t - 65 = 0
D = 729 + 2080 = 2809 = 53²
t = (27 - 53)/16 = - 13/8 t = (27 + 53) /16 = 5
x + 1/x = - 13/8 x + 1/x = 5
8x² + 13x + 8 = 0 x² - 5x + 1 = 0
D = 169 - 256 <0 D = 25 - 4 = 21<br> x = (5 - √21)/2 x = (5 + √21)/2