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

Задача №17539: Неравенство

lo g_{x - 1} (x + 1) - lo g_{x + 1} (x - 1) ⩾ 1 ⟺ \frac{ln ( x + 1 )}{ln ( x - 1 )} - \frac{2 ln ( x - 1 )}{ln ( x + 1 )} - 1 ⩾ 0 ⟺

\frac{ln ^{2} ( x + 1 ) - 2 ln ^{2} ( x - 1 ) - ln ( x - 1 ) ln ( x + 1 )}{ln ( x - 1 ) ln ( x + 1 )} ⩾ 0 ⟺

\frac{( ln ( x + 1 ) - 2 ln ( x - 1 ) ) ( ln ( x + 1 ) + ln ( x - 1 ) )}{ln ( x - 1 ) ln ( x + 1 )} ⩾ 0 ⟺

⎩ ⎨ ⎧ x > 1 \frac{( ( x + 1 ) - ( x - 1 ) ^{2} ) ( ( x + 1 ) - ( x - 1 ) ^{- 1} )}{( x - 2 ) x} ⩾ 0 ⟺ ⎩ ⎨ ⎧ x > 1 \frac{x ( 3 - x ) ( x - 2 ) ( x + 2 )}{( x - 2 ) x} ⩾ 0 ⟺ x \in (1, 2] \cup (2, 3]