已知abcd=1,求a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(da
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已知abcd=1,求a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(dab+da+d+1)的值.
a/(abc+ab+a+1)=a/(abc+ab+a+abcd)=1/(bc+b+1+bcd)
c/(cda+cd+c+1)=bc/(bcda+bcd+bc+b)=bc/(1+bcd+bc+b)
d/(dab+da+d+1)=bcd/(dabcb+dabc+bcd+bc)=bcd/(b+1+bcd+bc)
所以,
a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(dab+da+d+1)
=1/(bc+b+1+bcd)+b/(bc+b+1+bcd)+bc/(bc+b+1+bcd)+bcd/(bc+b+1+bcd)
=(bc+b+1+bcd)/(bc+b+1+bcd)
=1
c/(cda+cd+c+1)=bc/(bcda+bcd+bc+b)=bc/(1+bcd+bc+b)
d/(dab+da+d+1)=bcd/(dabcb+dabc+bcd+bc)=bcd/(b+1+bcd+bc)
所以,
a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(dab+da+d+1)
=1/(bc+b+1+bcd)+b/(bc+b+1+bcd)+bc/(bc+b+1+bcd)+bcd/(bc+b+1+bcd)
=(bc+b+1+bcd)/(bc+b+1+bcd)
=1
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