P(x)=ax^2(1-b)(1-c)/a^2(1-b)(1-c)+bx^2(1-a)(1-c)/b^2(1-a)(1-c)+cx^2(1-a)(1-b)/c^2(1-a)(1-b)

= x^2/a + x^2/b +x^2/c

P(x) = x^2(1/a+1/b+1/c)

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