Question

Решить уравнение :
2х/х-1 + 3/x+1=3x+1/х^2-1

Answer 1

2x/(x - 1) + 3/(x + 1) =(3x + 1)/(x² - 1)
ОДЗ:
x² - 1 ≠ 0
x ≠ ±1

2x(x + 1)/(x² - 1) + 3(x - 1)/(x² - 1) = (3x + 1)/(x² - 1)
(2x² + 2x + 3x - 3 - 3x - 1)/(x² - 1) = 0
2x² + 2x - 4 = 0
x² + x - 2 = 0
x1 + x2 = -1
x1•x2 = -2
x1 = -2
x2 = 1 - не уд. ОДЗ.
Ответ: х = -2.

Answer 2

${2xover x-1}+{3over x+1}={3x+1over x^2-1}\{2x^2+2x+3x-3over(x-1)(x+1)}={3x+1over(x-1)(x+1)}\2x^2+2x-4=0, xneq1, xneq-1\(x-1)(x+2)=0, xneq1, xneq-1\x=-2$