利用1/n*(n+1) = 1/n - 1/(n+1)计算1/(x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2)
问题描述:
利用1/n*(n+1) = 1/n - 1/(n+1)计算1/(x-2)(x-3)-2/(x-1)(x-3)+1/(x-1)(x-2)
答
1/(x-2)(x-3)=[1/(x-2)]-[1/(x-3)]
1/(x-1)(x-2)=[1/(x-1)]-[1/(x-2)]
于是1/(x-2)(x-3)+1/(x-1)(x-2)=[1/(x-1)]-[1/(x-3)]=1/(x-1)(x-3)
所以原式=-1/(x-1)(x-3)