6 дробь х+1 - 1 дробь х-1=1

6 / (х + 1) - 1 / (х-1) = 1 | * (x + 1) (x - 1)

6 (x - 1) - 1 (x+1) = 1 * (x+1) (x-1)

6x - 6 - x - 1 = x^2 - 1^2

5x - 7 = x^2 - 1

x^2 - 1 - 5x + 7 = 0

x^2 - 5x + 6 = 0

D = (-5) ^2 - 4*1 * 6 = 25 - 24 = 1

D>0 - два корня уравнения

х1 = ( - (-5) - √1) / (2*1) = (5 - 1) / 2 = 4/2 = 2

х2 = ( - (-5) + √1) / (2*1) = (5+1) / 2 = 6/2 = 3

Ответ: х1 = 2; х2 = 3.