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MathNet 2023-part-06 — 191 problems (EN–VI) Question 40

Math Olympiad Vault · MathNet 2023-part-06 — 191 problems (EN–VI)

Question 40

Simplify the expression over the set of real numbers: $$\left(\frac{1}{x^{4}-27 x}-\frac{1}{x^{4}-3 x^{3}}\right): \frac{x^{n+2}-9 x^{n}}{x^{n+5}+3 x^{n+4}+9 x^{n+3}} ;\ x \neq 0,3,-3.$$