先化简再求值1/x+2-x²+2x+1/x+2÷x²-1/x-1,其中x=根号2-2先化简再求值1/x+2-x²+2x+1/x+2÷x²-1/x-1,其中x=根号2-2
问题描述:
先化简再求值1/x+2-x²+2x+1/x+2÷x²-1/x-1,其中x=根号2-2
先化简再求值1/x+2-x²+2x+1/x+2÷x²-1/x-1,其中x=根号2-2
答
1/(x+2) - (x²+2x+1)/(x+2) ÷(x²-1)/(x-1)=1/(x+2) - (x+1)²/(x+2) ÷ (x+1)=1/(x+2) - (x+1)/(x+2)=(1-x-1)/(x+2)=-x/(x+2)=-(根号2 -2)/(根号2-2+2)=(2-根号2)/根号2=根号2 -1