原式=(a+b)/(a-c)(b-c)+(b+c)/(a-b)(a-c)-(c+a)/(b-c)(a-b)
=(a+b)(a-b)/(a-c)(a-b)(b-c)+(b+c)(b-c)/(a-b)(a-c)(b-c)-(c+a)(a-c)/(b-c)(a-b) (a-c)
=[(a^2-b^2)+(b^2-c^2)-(a^2-c^2)]/(b-c)(a-b) (a-c)
=0