作业帮若x为x²-2x-2=0的正整数根,求(x²-1)/(x²+x)÷[x-(2x-1)/x]
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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