化简求值:(x+(x/x平方-1)÷(2+(1/x-1)-(1/x+1)选入一个合适的数代入求值~
问题描述:
化简求值:(x+(x/x平方-1)÷(2+(1/x-1)-(1/x+1)选入一个合适的数代入求值~
答
[x+x/(x²-1)]÷[2+1/(x-1)-1/(x+1)]
=[x(x²-1)+x]/(x²-1) ÷[2+[(x+1)-(x-1)]/(x²-1)}
=x³/(x²-1) ÷[2+2/(x²-1)]
=x³/(x²-1) ÷{[2(x²-1)+2]/(x²-1)}
=x³/(x²-1) ×(x²-1)/(2x²)
=x/2
分母x²-1≠0,x≠±1
取x=2,原式=2/2=1