解：a/(m+2) +b/(m-2)=4m/(m²-4)[a(m-2)+b(m+2)]/[(m+2)(m-2)]=4m/(m²-4)[(a+b)m-2(a-b)]/(m²-4)=4m/(m²-4)等式两边分母相同，要分子对于任意m恒成立，只有a+b=4-2(a-b)=0解得a=2，b=2√(ab)=√(2×2)=√4=2
