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先化简,再求值:x^2+2x+1/x+2÷x^2-1/x-1-1-x-x^2/x+2,其中x=2014
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先化简,再求值:x^2+2x+1/x+2 ÷x^2-1/x-1 - 1-x-x^2/x+2,其中x=2014
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解
(x²+2x+1)/(x+2)÷(x²-1)/(x-1)-(1-x-x²)/(x+2)
=(x+1)²/(x+2)÷(x-1)(x+1)/(x-1)-(1-x-x²)/(x+2)
=(x+1)²/(x+2)×1/(x+1)-(1-x-x²)/(x+2)
=(x+1)/(x+2)-(1-x-x²)/(x+2)
=(x+1-1+x+x²)/(x+2)
=(x²+2x)/(x+2)
=x
=2014
(x²+2x+1)/(x+2)÷(x²-1)/(x-1)-(1-x-x²)/(x+2)
=(x+1)²/(x+2)÷(x-1)(x+1)/(x-1)-(1-x-x²)/(x+2)
=(x+1)²/(x+2)×1/(x+1)-(1-x-x²)/(x+2)
=(x+1)/(x+2)-(1-x-x²)/(x+2)
=(x+1-1+x+x²)/(x+2)
=(x²+2x)/(x+2)
=x
=2014
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