Verified answer

5/(х-1) - 3/(х+1) = 15/(х²-1),

5*(х+1)/(х²-1) - 3*(х-1)/(х²-1) =15/(х²-1),

(5х+5)/(х²-1) - (3х-3)/(х²-1) = 15/(х²-1),

5х+5 - 3х+3 = 15,

2х = 15-5-3,

2х = 7,

х = 3,5  (или 3 1/2),

х - 1 ≠ 0,   х + 1 ≠ 0,

х ≠ 1,        х ≠ -1,

проверка корней:

5/(3,5-1) - 3/(3,5+1) = 15/(3,5²-1),

5/(2,5) - 3/(4,5) = 15/(11,25),

2 - 2/3 = 4/3,

1 3/3 - 2/3 = 1 1/3,

1 1/3 = 1 1/3