Решите неравенство _(x-1)(x+1) - _(sqrt(x+1))(x-1) 1 .

_(x-1)(x+1) - _(sqrt(x+1))(x-1) 1 (ln(x+1))/(ln(x-1)) - (2ln(x-1))/(ln(x+1)) - 1 0 (ln^2(x+1) - 2ln^2(x-1) - ln(x-1)ln(x+1))/(ln(x-1)ln(x+1)) 0 (( ln(x+1) - 2ln(x-1) )( ln(x+1) + ln(x-1) ))/(ln(x-1)ln(x+1)) 0 cases x > 1 (( (x+1) - (x-1)^2 )( (x+1) - (x-1)^(-1) ))/((x-2)x) 0 cases cases x > 1 (x(3-x)(x-sqrt(2))(x+sqrt(2)))/((x-2)x) 0 cases x in (1, sqrt(2)] U (2, 3]

\( x \in (1, \sqrt{2}] \cup (2, 3] \)