分解因式：a^2/(a-b)(a-c)+b^2 /(b-a)(b-c)+c^2 /(c-a)(c-b)
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a^2/(a-b)(a-c)+b^2 /(b-a)(b-c)+c^2 /(c-a)(c-b)
=a²/[(a-b)(a-c)]-b²/[(a-b)(b-c)]+c²/[(a-c)(b-c)]
=[a²(b-c)-b²(a-c)+c²(a-b)]/[(a-b)(b-c)(a-c)]
=[(a²b-a²c-ab²+b²c+c²(a-b)]/[(a-b)(b-c)(a-c)]
=[(a²b-ab²)-(a²c-b²c)+c²(a-b)]/[(a-b)(b-c)(a-c)]
=(a-b)[ab-ac-bc+c²]/[(a-b)(b-c)(a-c)]
=(a-b)[(ab-bc)-(ac-c²)]/[(a-b)(b-c)(a-c)]
=(a-b)(b-c)(a-c)/[(a-b)(b-c)(a-c)]
=1
=a²/[(a-b)(a-c)]-b²/[(a-b)(b-c)]+c²/[(a-c)(b-c)]
=[a²(b-c)-b²(a-c)+c²(a-b)]/[(a-b)(b-c)(a-c)]
=[(a²b-a²c-ab²+b²c+c²(a-b)]/[(a-b)(b-c)(a-c)]
=[(a²b-ab²)-(a²c-b²c)+c²(a-b)]/[(a-b)(b-c)(a-c)]
=(a-b)[ab-ac-bc+c²]/[(a-b)(b-c)(a-c)]
=(a-b)[(ab-bc)-(ac-c²)]/[(a-b)(b-c)(a-c)]
=(a-b)(b-c)(a-c)/[(a-b)(b-c)(a-c)]
=1
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