Question

(Х+2)/(Х-2) +(Х-2)/(Х+2)=13/6

Answer 1

$frac{x+2}{x-2}+ frac{x-2}{x+2}= frac{13}{6}\\ frac{(x+2)(x+2)+(x-2)(x-2)}{x^2-4}= frac{13}{6} \\frac{x^2+4x+4+x^2-4x+4}{x^2-4}= frac{13}{16}\\frac{2x^2+8}{x^2-4}= frac{13}{6}$

ОДЗ:

$x^2-4neq 0\ xneq pm2$


$12x^2+48=13x^2-52\ 12x^2-13x^2=-52-48\ x^2=100\ x_{1/2}=pm10$


Ответ: $x_1=-10; x_2=10$