答：
y=x^2-1
m=(3x+y-5)/(x-1)+(x+3y-7)/(y-2)
=(3x+x^2-1-5)/(x-1)+(x+3x^2-3-7)/(x^2-1-2)
=(x^2+3x-6)/(x-1)+(3x^2+x-10)/(x^2-3)
m'(x)=(2x+3)/(x-1)-(x^2+3x-6)/(x-1)^2+(6x+1)/(x^2-3)-(6x^3+2x^2-20x)/(x^2-3)^2
=(x^2-2x+3)[1/(x-1)^2-1/(x^2-3)^2]
=(x^2-2x+3)(x^2+x-4)(x^2-x-2)/[(x-1)^2*(x^2-3)^2]
因為x>√3,因此只有x^2-x-2的值可能為0
令m‘(x)=0,則：x^2-x-2=0,解得：x=2（x=-1不符合舍去）
所以：
當(dāng)√3=0,m(x)是增函數(shù).
所以：當(dāng)x=2時,m取得最小值為8
把x=2代入拋物線方程y=x^2-1得y=3
所以點(diǎn)P坐標(biāo)為(2,3).