
先化简,再求值:{[(x*x+4)/x]-4}/(x*x-4)/(x*x+2x),其中x=-1
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解:
原式={[(x²+4)/x]-4}÷[(x²-4)/(x²+2x)]
={(x²+4)/x-(4x/x)}÷{(x-2)(x+2)/[x(x+2)]}
=[(x²+4-4x)/x]÷[(x-2)/x]
=[(x-2)²/x]×[x/(x-2)]
=x-2
=-1-2
=-3
原式={[(x²+4)/x]-4}÷[(x²-4)/(x²+2x)]
={(x²+4)/x-(4x/x)}÷{(x-2)(x+2)/[x(x+2)]}
=[(x²+4-4x)/x]÷[(x-2)/x]
=[(x-2)²/x]×[x/(x-2)]
=x-2
=-1-2
=-3
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