分式化简1-[(x-1)/x]÷{[x/(x+2)] -[1/(x^2+2x)]}

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分式化简1-[(x-1)/x]÷{[x/(x+2)] -[1/(x^2+2x)]}

分式化简1-[(x-1)/x]÷{[x/(x+2)] -[1/(x^2+2x)]}
分式化简1-[(x-1)/x]÷{[x/(x+2)] -[1/(x^2+2x)]}

分式化简1-[(x-1)/x]÷{[x/(x+2)] -[1/(x^2+2x)]}
1-[(x-1)/x]÷{[x/(x+2)] -[1/(x^2+2x)]}
=(x-x+1)/x÷x/{(x+2) -1/[x(x+2)]}
=1/x÷[(x-2)(x+2)/x(x+2)-1/x(x+2)]
=1/x÷[x²-2²-1/x(x+2)]
=1/x÷(x² -5)/x(x+2)
=1/x×x(x+2)/(x² -5)
=(x+2)/(x² -5)