若m+n-p=0，则m(1n−1p)+n(1m−1p)−p(1m+1n)的值等于．

Question

若m+n-p=0，则m((1)/(n)−(1)/(p))+n((1)/(m)−(1)/(p))−p((1)/(m)+(1)/(n))的值等于______．

Answer 1

则m((1)/(n)−(1)/(p))+n((1)/(m)−(1)/(p))−p((1)/(m)+(1)/(n))=(m)/(n)-(m)/(p)+(n)/(m)-(n)/(p)-(p)/(m)-(p)/(n)=(m−p)/(n)+(n−p)/(m)-(m+n)/(p)
由题意可得：m-p=-n，m-p=-n，n-p=-m，m+n=p，
∴可得：m((1)/(n)−(1)/(p))+n((1)/(m)−(1)/(p))−p((1)/(m)+(1)/(n))=-1-1-1=-3．
故答案为：-3．