Given the function f (x) = alnx / (x + 1) + B / x, the tangent equation of curve y = f (x) at point (1, f (1)) is x + 2y-3 = 0 (1) Finding the value of a and B (2) If x ＞ 0 and X ≠ 1, f (x) ＞ LNX / (x-1) + K / x, find the value range of K I have solved the first problem, a = b = 1. The second problem uses partial derivation, let H (x) = 1 / (1-x ^ 2) [2lnx + (k-1) (x ^ 2-1) / x], and then let g (x) = 2lnx + (k-1) (x ^ 2-1) / X to solve the derivation. What should I do next?

Given the function f (x) = alnx / (x + 1) + B / x, the tangent equation of curve y = f (x) at point (1, f (1)) is x + 2y-3 = 0 (1) Finding the value of a and B (2) If x ＞ 0 and X ≠ 1, f (x) ＞ LNX / (x-1) + K / x, find the value range of K I have solved the first problem, a = b = 1. The second problem uses partial derivation, let H (x) = 1 / (1-x ^ 2) [2lnx + (k-1) (x ^ 2-1) / x], and then let g (x) = 2lnx + (k-1) (x ^ 2-1) / X to solve the derivation. What should I do next?

This is the 2011 national new curriculum standard 21 questions, this question is very complex, need to discuss the K line, as follows, if you agree with my answer, please click "adopt as a satisfactory answer", I wish learning progress!

Given the function f (x) = 1 x-alnx. (a ∈ R) (1) when a = - 1, try to determine the monotonicity of function f (x) in its domain of definition; (2) find the minimum value of function f (x) on (0, e)

(1) When a = - 1, f (x) = LX + LNX, X ∈ (0, + ∞), then f '(x) = x − 1x2, ∵ when 0 < x < 1, f' (x) ∵ 0; when x > 1, f '(x) ∵ 0

The function f (x) = alnx + X is known
The known function f (x) = alnx + X & # 178; (a is a constant)
(1) if a = - 2, the increasing function of function f (x) on (1, + ∞) is proved
(2) if a ≥ - 2, find the minimum value of function f (x) on [1. E] and the corresponding x value
Detailed steps, thank you

(1) If a = - 2 is substituted, then f = - 2lnx + x ^ 2
The derivation of X can be obtained as follows
F '= - 2 / x + 2x = 2 (x-1 / x), because x > 1, then 0