解析：M=(a+1)/(a-2)=(a-2+3)/(a-2)=1+3/(a-2),
∵2＜a＜3,∴0＜a-2＜1,3/(a-2)＞3,则M＞4;
N=-3x^2+4√3*x=-3(x-2√3)^2+4/3
∵0＜x＜4√3-3,∴N≤4/3
那么M＞N.