证明：∵f(x)=x³/(x²-1)²,且x∈(1,+∞)∴f'(x)={(x²-1)²(x³)'-x³[(x²-1)²]'}/(x²-1)^4=-x²(x²+3)/(x²-1)³ (化简整理)∵x∈(1,+∞),有x²...