化简：x+2分之x²+2x+1除以x-1分之x²-1-x+2分之x
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(x²+2x+1)/(x+2)÷(x²-1)/(x-1)-x/(x+2)
=(x+1)²/(x+2)÷[(x-1)(x+1)/(x-1)]-x/(x+2)
=(x+1)²/(x+2)÷[(x-1)(x+1)/(x-1)]-x/(x+2)
=(x+1)²/(x+2)÷(x+1)-x/(x+2)
=(x+1)²/(x+2)×1/(x+1)-x/(x+2)
=(x+1)/(x+2)-x/(x+2)
=(x+1-x)/(x+2)
=1/(x+2)
=(x+1)²/(x+2)÷[(x-1)(x+1)/(x-1)]-x/(x+2)
=(x+1)²/(x+2)÷[(x-1)(x+1)/(x-1)]-x/(x+2)
=(x+1)²/(x+2)÷(x+1)-x/(x+2)
=(x+1)²/(x+2)×1/(x+1)-x/(x+2)
=(x+1)/(x+2)-x/(x+2)
=(x+1-x)/(x+2)
=1/(x+2)
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