一条分式数学题,希望能有高手为我详细的解答.已知:a+b+c=0且(b-c/a)+(c-a/b)+(a-b/c)=0,求证:(bc+b-c/b^2c^2)+(ca+c-a/c^2a^2)+(ab+a-b/a^2b^2)=0.
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![一条分式数学题,希望能有高手为我详细的解答.已知:a+b+c=0且(b-c/a)+(c-a/b)+(a-b/c)=0,求证:(bc+b-c/b^2c^2)+(ca+c-a/c^2a^2)+(ab+a-b/a^2b^2)=0.](/uploads/image/z/1036497-57-7.jpg?t=%E4%B8%80%E6%9D%A1%E5%88%86%E5%BC%8F%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E5%B8%8C%E6%9C%9B%E8%83%BD%E6%9C%89%E9%AB%98%E6%89%8B%E4%B8%BA%E6%88%91%E8%AF%A6%E7%BB%86%E7%9A%84%E8%A7%A3%E7%AD%94.%E5%B7%B2%E7%9F%A5%3Aa%2Bb%2Bc%3D0%E4%B8%94%28b-c%2Fa%29%2B%28c-a%2Fb%29%2B%28a-b%2Fc%29%3D0%2C%E6%B1%82%E8%AF%81%3A%28bc%2Bb-c%2Fb%5E2c%5E2%29%2B%28ca%2Bc-a%2Fc%5E2a%5E2%29%2B%28ab%2Ba-b%2Fa%5E2b%5E2%29%3D0.)
一条分式数学题,希望能有高手为我详细的解答.已知:a+b+c=0且(b-c/a)+(c-a/b)+(a-b/c)=0,求证:(bc+b-c/b^2c^2)+(ca+c-a/c^2a^2)+(ab+a-b/a^2b^2)=0.
一条分式数学题,希望能有高手为我详细的解答.
已知:a+b+c=0且(b-c/a)+(c-a/b)+(a-b/c)=0,求证:(bc+b-c/b^2c^2)+(ca+c-a/c^2a^2)+(ab+a-b/a^2b^2)=0.
一条分式数学题,希望能有高手为我详细的解答.已知:a+b+c=0且(b-c/a)+(c-a/b)+(a-b/c)=0,求证:(bc+b-c/b^2c^2)+(ca+c-a/c^2a^2)+(ab+a-b/a^2b^2)=0.
(bc+b-c)/(b^2c^2)+(ca+c-a)/(c^2a^2)+(ab+a-b)/(a^2b^2)
=a^2(bc+b-c)/(b^2c^2a^2)+b^2(ca+c-a)/(c^2a^2b^2)+c^2(ab+a-b-1)/(a^2b^2c^2)
=(a^2bc+a^2b-a^2c+b^2ac+b^2c-b^2a+c^2ab+c^aa-c^2b)/(a^2b^2c^2)
=[(a+b+c)abc+a^2b-a^2c+b^2c-b^2a+c^2a-c^2b)]/(a^2b^2c^2)
=[(a+b+c)abc+a^2b-b^2a+a^2c-c^2a+b^2c-c^2b)]/(a^2b^2c^2)
=[(a+b+c)abc+(a-b)ab+(b-c)bc+(c-a)ac]/(a^2b^2c^2)
={(a+b+c)abc+abc[(b-c)/a+(c-a)/b+(a-b)/c]}/(a^2b^2c^2)
=0