一道数学题,高手请进(答对了有分哦)若a+b=c+d,化简:abcd(1/a+1/b+1/c+1/d)除以(ab+cd).
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![一道数学题,高手请进(答对了有分哦)若a+b=c+d,化简:abcd(1/a+1/b+1/c+1/d)除以(ab+cd).](/uploads/image/z/8866911-39-1.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%2C%E9%AB%98%E6%89%8B%E8%AF%B7%E8%BF%9B%EF%BC%88%E7%AD%94%E5%AF%B9%E4%BA%86%E6%9C%89%E5%88%86%E5%93%A6%EF%BC%89%E8%8B%A5a%2Bb%3Dc%2Bd%2C%E5%8C%96%E7%AE%80%EF%BC%9Aabcd%281%2Fa%2B1%2Fb%2B1%2Fc%2B1%2Fd%29%E9%99%A4%E4%BB%A5%EF%BC%88ab%2Bcd%EF%BC%89.)
一道数学题,高手请进(答对了有分哦)若a+b=c+d,化简:abcd(1/a+1/b+1/c+1/d)除以(ab+cd).
一道数学题,高手请进(答对了有分哦)
若a+b=c+d,化简:abcd(1/a+1/b+1/c+1/d)除以(ab+cd).
一道数学题,高手请进(答对了有分哦)若a+b=c+d,化简:abcd(1/a+1/b+1/c+1/d)除以(ab+cd).
abcd(1/a+1/b+1/c+1/d)=bcd+acd+abd+abc
=(a+b)cd+(c+d)ab=(a+b)(cd+ab)
所以原式化简为a+b 或c+d
abcd(1/a+1/b+1/c+1/d)
=abc+bcd+cda+dab
=ab(c+d)+cd(a+b).
(因为a+b=c+d,提取公因式,有:)
=(ab+cd)(a+b).
所以原式=(ab+cd)(a+b)/(ab+cd)=a+b.
abcd(1/a+1/b+1/c+1/d)除以(ab+cd)
=bcd+acd+abd+abc/(ab+cd)
=(b+a)cd+(d+c)ab/(ab+cd)
=(a+b)(cd+bc)/(ab+cd)
=a+b
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abcd(1/a+1/b+1/c+1/d)
=abc+bcd+cda+dab
=ab(c+d)+cd(a+b).
(因为a+b=c+d,提取公因式,有:)
=(ab+cd)(a+b).
所以原式=(ab+cd)(a+b)/(ab+cd)=a+b.
解:abcd*(1/a+1/b+1/c+1/d)/(ab+cd)
=abcd*((a+b)/ab+(c+d)/cd)/(ab+cd)
=abcd*(cd(a+b)+ab(c+d))/abcd*(1/(ab+cd))
又a+b=c+d
=(ab+cd)9*(a+b)*(1/(ab+cd))
=a+b=c+d