Question

Решите дробно-рациональное уравнение
(x+3)/(x-3) + (x-3)/(x+3) = 10/3

Answer 1

$\frac{x+3}{x-3} + \frac{x-3}{x+3} = \frac{10}{3}\\ \frac{(x+3)^2 + (x-3)^2}{(x-3)(x+3)} = \frac{10}{3} \\ 10(x^2-9) = 3(x^2+6x+9+x^2-6x+9)\\ 10x^2 - 90 = 6x^2 + 54\\ 4x^2 = 144\\ x^2 = 36\\ x = \pm6$