Question

先化简在求值，（x/x-1-1/x²-x）÷（x+1）。其中x=√2.

Answer 1

您好：

（x/x-1-1/x²-x）÷（x+1)
=（x²/x²-x-1/x²-x）÷（x+1)
=（x²-1）/x(x-1)÷（x+1）
=(x+1)(x-1)/x(x+1)(x-1)
=1/x
=1/√2
=(√2)/2

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Answer 2

[x/(x-1)-1/(x²-x)]÷(x+1)
=[x²/x(x-1)-1/x(x-1)]÷(x+1)
=[(x²-1)/x(x-1)]÷(x+1)
=[(x+1)(x-1)/x(x-1)]÷(x+1)
=[(x+1)/x]×1/(x+1)
=1/x
=1/√2=√2/2.

Answer 3

原式=(x²-1)/x(x-1)*1/(x+1)
=(x+1)(x-1)/x(x-1)*1/(x+1)
=(x+1)/x*1/(x+1)
=1/x
=1/√2
=√2/2