Question 171
For every positive integer $n$, determine the greatest possible value of the quotient
$$
\frac{1 - x^n - (1-x)^n}{x(1-x)^n + (1-x)x^n}
$$
where $0 \lt x \lt 1$.
$$
\frac{1 - x^n - (1-x)^n}{x(1-x)^n + (1-x)x^n}
$$
where $0 \lt x \lt 1$.
MathNet 2016-part-05 — 184 problems (EN–VI) Question 171
Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)