先化简,再求值先化简,再求值{1-x/x+1-1}÷2x/x²-1 ,其中x=1-√2

问题描述:

先化简,再求值先化简,再求值{1-x/x+1-1}÷2x/x²-1 ,其中x=1-√2

[(1-x)/(x+1)-1]÷2x/(x²-1)=[(1-x-x-1)/(x+1)]÷2x/(x²-1)=-2x/(x+1)÷2x/(x²-1)=-2x/(x+1)*(x²-1)/2x=-(x²-1)/(x+1)=-(x-1)(x+1)/(x+1)=-(x-1)=1-x=1-(1-√2 )=1-1+√2 =√2