若abcd=1 求证a/abc+ab+a+1 + b/bcd+bc+d+1 + c/dca+cd+1 + d/dab+da+d+1=1

问题描述:

若abcd=1 求证a/abc+ab+a+1 + b/bcd+bc+d+1 + c/dca+cd+1 + d/dab+da+d+1=1

a/(abc+ab+a+1)+b/(bcd+bc+b+1)+c/(cda+cd+c+1)+d/(dab+da+d+1) =a/(1/d+ab+a+1)+b/(bcd+bc+b+1)+c/(1/b+cd+c+1)+d/(dab+da+d+1) =ad/(abd+ad+d+1)+b/(bcd+bc+b+1)+bc/(bcd+bc+b+1)+d/(dab+da+d+1) =(ad+d)/(abd+ad+...