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4.化简(m-c)/[(m-a)(m-b)]+(b-c)/[(a-b)(m-b)]+(b-c)/[(b-a)(m-a)]5.化简a/[a-b)(a-c)]+b/[(b-c)(b-a)]+c/[(c-a)(c-b)]
题目详情
4.化简(m-c)/[(m-a)(m-b)]+(b-c)/[(a-b)(m-b)]+(b-c)/[(b-a)(m-a)]
5.化简a/[a-b)(a-c)]+b/[(b-c)(b-a)]+c/[(c-a)(c-b)]
5.化简a/[a-b)(a-c)]+b/[(b-c)(b-a)]+c/[(c-a)(c-b)]
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答案和解析
4.化简(m-c)/[(m-a)(m-b)]+(b-c)/[(a-b)(m-b)]+(b-c)/[(b-a)(m-a)]
=(m-c)/[(m-a)(m-b)]+(b-c)/[(a-b)(m-b)]-(b-c)/[(a-b)(m-a)]
=(m-c)/[(m-a)(m-b)]+[(b-c)/(a-b)][1/(m-b)-1/(m-a)]
=(m-c)/[(m-a)(m-b)]+[(b-c)/(a-b)]*(a-b)/[(m-b)(m-a)]
=(m-c)/[(m-a)(m-b)]+(b-c)/[(m-b)(m-a)]
=(m+b-2c)/[(m-b)(m-a)]
5.化简a/[a-b)(a-c)]+b/[(b-c)(b-a)]+c/[(c-a)(c-b)]
=a/[a-b)(a-c)]-b/[(b-c)(a-b)]+c/[(a-c)(b-c)]
=[a(b-c)-b(a-c)+c(a-b)]/[(a-b)(a-c)(b-c)]
=0/[(a-b)(a-c)(b-c)]
=0
=(m-c)/[(m-a)(m-b)]+(b-c)/[(a-b)(m-b)]-(b-c)/[(a-b)(m-a)]
=(m-c)/[(m-a)(m-b)]+[(b-c)/(a-b)][1/(m-b)-1/(m-a)]
=(m-c)/[(m-a)(m-b)]+[(b-c)/(a-b)]*(a-b)/[(m-b)(m-a)]
=(m-c)/[(m-a)(m-b)]+(b-c)/[(m-b)(m-a)]
=(m+b-2c)/[(m-b)(m-a)]
5.化简a/[a-b)(a-c)]+b/[(b-c)(b-a)]+c/[(c-a)(c-b)]
=a/[a-b)(a-c)]-b/[(b-c)(a-b)]+c/[(a-c)(b-c)]
=[a(b-c)-b(a-c)+c(a-b)]/[(a-b)(a-c)(b-c)]
=0/[(a-b)(a-c)(b-c)]
=0
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