作业帮若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/09 10:46:17
![若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]](/uploads/image/z/10921869-45-9.jpg?t=%E8%8B%A5x%E4%B8%BAx%26%23178%3B-2x-2%3D0%E7%9A%84%E6%AD%A3%E6%95%B4%E6%95%B0%E6%A0%B9%2C%E6%B1%82%28x%26%23178%3B-1%29%2F%28x%26%23178%3B%2Bx%29%C3%B7%5Bx-%282x-1%29%2Fx%5D)
若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]
若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]
若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]
(x²-1)/(x²+x)÷[x-(2x-1)/x]
=(x+1)(x-1)/x(x+1)÷[(x²-2x+1)/x]
=(x-1)/x÷[(x-1)²/x]
=1/(x-1)
x为x²-2x-2=0的正整数根,x-1≥0
x²-2x+1-3=0
x²-2x+1=3
(x-1)²=3
x-1=√3
原式=1/(x-1)=1/√3=√3/3