Question

Решение уравнения x+1/x-1+x-1/x+1=3

Answer 1

$\tt\displaystyle \frac{x+1}{x-1}+\frac{x-1}{x+1}=3|\cdot (x-1)(x+1)\\ODZ: \left \{ {{x\neq1} \atop {x\neq-1}} \right. \\(x+1)^2+(x-1)^2=3(x^2-1)\\x^2+2x+1+x^2-2x+1-3x^2+3=0\\-x^2+5=0\\x^2=5\\\left [{ {{x=\sqrt{5}} \atop {x=-\sqrt{5}}} \right.$

Ответ: $-\sqrt{5};\sqrt{5}$