当X=根号2-2时,求(X²-1)(2/X-1 +1/X+1)的值
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当X=根号2-2时,求(X²-1)(2/X-1 +1/X+1)的值
当x=√2-2 时,求(x²-1)(x-1分之2 + x+1分之1)的值
当x=√2-2 时,求(x²-1)(x-1分之2 + x+1分之1)的值
![当X=根号2-2时,求(X²-1)(2/X-1 +1/X+1)的值](/uploads/image/z/19433774-38-4.jpg?t=%E5%BD%93X%3D%E6%A0%B9%E5%8F%B72-2%E6%97%B6%2C%E6%B1%82%EF%BC%88X%26%23178%3B-1%EF%BC%89%EF%BC%882%2FX-1+%2B1%2FX%2B1%EF%BC%89%E7%9A%84%E5%80%BC)
答:
(x^2-1)*[2/(x-1)+1/(x+1)]
=(x^2-1)*[2(x+1)/(x^2-1)+(x-1)/(x^2-1)]
=(x^2-1)*(2x+2+x-1)/(x^2-1)
=3x+1
=3(√2-2)+1
=3√2-5
(x^2-1)*[2/(x-1)+1/(x+1)]
=(x^2-1)*[2(x+1)/(x^2-1)+(x-1)/(x^2-1)]
=(x^2-1)*(2x+2+x-1)/(x^2-1)
=3x+1
=3(√2-2)+1
=3√2-5
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