先化简，再求值:x^2-1/(x+2)(x-1)÷[1+1/(x^2+2x)]
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(x^2-1)/(x+2)(x-1) ÷ [1+1/(x^2+2x)]
=(x+1)(x-1)/(x+2)(x-1) ÷ [(x^2+2x+1)/(x^2+2x)]
=(x+1)(x-1)/(x+2)(x-1) * (x^2+2x)/(x^2+2x+1)
=(x+1)(x-1)/(x+2)(x-1) * x(x+2)/(x+1)^2
=x /(x+1)
=(x+1)(x-1)/(x+2)(x-1) ÷ [(x^2+2x+1)/(x^2+2x)]
=(x+1)(x-1)/(x+2)(x-1) * (x^2+2x)/(x^2+2x+1)
=(x+1)(x-1)/(x+2)(x-1) * x(x+2)/(x+1)^2
=x /(x+1)
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(x^2-1)/(x+2)(x-1)÷[1+1/(x^2+2x)]
=(x-1)(x+1)/(x+2)(x-1)÷[1+1/(x^2+2x)]
=(x+1)/(x+2)÷[(x^2+2x+1)/(x^2+2x)]
=(x+1)/(x+2)÷[(x+1)^2/(x^2+2x)]
=(x+1)/(x+2)*(x^2+2x)/(x+1)^2
=(x+1)/(x+2)*x(x+2)/(x+1)^2
=(x+1)*x/(x+1)^2
=x/(x+1)
=(x-1)(x+1)/(x+2)(x-1)÷[1+1/(x^2+2x)]
=(x+1)/(x+2)÷[(x^2+2x+1)/(x^2+2x)]
=(x+1)/(x+2)÷[(x+1)^2/(x^2+2x)]
=(x+1)/(x+2)*(x^2+2x)/(x+1)^2
=(x+1)/(x+2)*x(x+2)/(x+1)^2
=(x+1)*x/(x+1)^2
=x/(x+1)
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