a^2/(a−b)(a−c)+b^2/(b−c)(b−a)+c^2/(c−a)(c−b)
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Step-by-step explanation:
a(b
2
+c
2
)+b(c
2
+a
2
)+c(a
2
+b
2
)+2abc
=ab
2
+ac
2
+bc
2
+ba
2
+ca
2
+cb
2
+2abc
=ba
2
+ca
2
+ab
2
+ac
2
+2abc+bc
2
+cb
2
=a
2
(b+c)+a(b
2
+c
2
+2bc)+bc(c+b)
=a
2
(b+c)+(b+c)
2
+bc(b+c)
=(b+c)[(a
2
+a(b+c)+bc]
=(b+c)[a
2
+ab+ac+bc]
=(b+c)[a(a+b)+c(a+b)]
=(b+c)(a+b)(a+c)
=(a+b)(b+c)(c+a)
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