化简求值 X/X+2 - X2+2X+1/X+2 ÷ X2-1/X-2 其中X=√3-2
问题描述：
化简求值 X/X+2 - X2+2X+1/X+2 ÷ X2-1/X-2 其中X=√3-2
答
X/(X+2) - (X^2+2X+1)/(X+2) ÷[( X^2-1)/(X-2)]
=x/(x-2)-(x+1)^2/(x+2)×(x-2)/[(x+1)(x-1)]
=x(x-1)/[(x-1)(x+2)]-(x+1)(x-2)/[(x-1)(x+2)]
=2/[(x-1)(x+2)]
=2/[(√3-2-1)(√3-2+2)]
=2/(3-3√3)
=-1-√3 /3
答
X/X+2 - X2+2X+1/X+2 ÷ X2-1/X-2
=[x/(x+2)]-[(x+1)^2/(x+2)]*{(x-2)/[(x+1)(x-1)]}
=[x/(x+2)]-{(x+1)(x-2)/[(x+2)*(x-1)]}
={1/(x+2)}*{x-[(x^2-x-2)/(x-1)]}
={1/(x+2)}*{2/(x-1)}
=2/[(x+2)(x-1)]
=2/[√3*(√3-3)]
=-(1+√3)/3
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