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化简b-c/(a-b)(a-c)+c-a/(b-c)(b-a)+a-b/(c-a)(c-b)+2/b-a-2/c-a
题目详情
化简b-c/(a-b)(a-c)+c-a/(b-c)(b-a)+a-b/(c-a)(c-b)+2/b-a-2/c-a
▼优质解答
答案和解析
(b-c)/(a-b)(a-c)+(c-a)/(b-c)(b-a)+(a-b)/(c-a)(c-b)+2/(b-a)-2/(c-a)
=(b-c)/(a-b)(a-c)+(a-c)(b-c)/(a-b)+(a-b)/(a-c)(b-c)-2/(a-b)+2/(a-c)
=[(b-c)²+(a-c)²+(a-b)²]/(a-b)(a-c)(b-c)+[2(a-b)-2(a-c)]/(a-c)(a-b)
=[(b-c)²+(a-c)²+(a-b)²]/(a-b)(a-c)(b-c)-2(b-c)/(a-c)(a-b)
=[(b-c)²+(a-c)²+(a-b)²-2(b-c)²]/(a-b)(a-c)(b-c)
=[(a-c)²+(a-b)²-(b-c)²]/(a-b)(a-c)(b-c)
=[(a-c)²+(a-b+b-c)(a-b-b+c)]/(a-b)(a-c)(b-c)
=(a-c)(a-c+a+c-2b)/(a-b)(a-c)(b-c)
=2(a-b)/(a-b)(b-c)
=2/(b-c)
=(b-c)/(a-b)(a-c)+(a-c)(b-c)/(a-b)+(a-b)/(a-c)(b-c)-2/(a-b)+2/(a-c)
=[(b-c)²+(a-c)²+(a-b)²]/(a-b)(a-c)(b-c)+[2(a-b)-2(a-c)]/(a-c)(a-b)
=[(b-c)²+(a-c)²+(a-b)²]/(a-b)(a-c)(b-c)-2(b-c)/(a-c)(a-b)
=[(b-c)²+(a-c)²+(a-b)²-2(b-c)²]/(a-b)(a-c)(b-c)
=[(a-c)²+(a-b)²-(b-c)²]/(a-b)(a-c)(b-c)
=[(a-c)²+(a-b+b-c)(a-b-b+c)]/(a-b)(a-c)(b-c)
=(a-c)(a-c+a+c-2b)/(a-b)(a-c)(b-c)
=2(a-b)/(a-b)(b-c)
=2/(b-c)
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