Splitting a Logarithm

★ 8/10calculus Monotonicity Logarithms inequality Discriminant

Problem

Find all $k$ such that

\frac{\ln x}{x+1} + \frac1x > \frac{\ln x}{x-1} + \frac{k}{x}

holds for all $x > 0$ with $x \ne 1$ .

Answer

Solution

Difficulty	8/10
Topics	calculus, Monotonicity, Logarithms, inequality, Discriminant

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