先化简,再求值,初三的
先化简,再求值,【1/(x-y)】-【1/(x+y)】/【xy²/(x²-y²)】,其中x=√2+1,y=√2-1...
先化简,再求值,【1/(x-y)】-【1/(x+y)】/【xy²/(x²-y²)】,其中x=√2+1,
y=√2-1 展开
y=√2-1 展开
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先化简,再求值:【1/(x-y)】-【1/(x+y)】/【xy²/(x²-y²)】,其中x=√2+1,
y=√2-1
解:【1/(x-y)】-【1/(x+y)】/【xy²/(x²-y²)】
=(x+y-x+y)/(x^2-y^2)*(x^2-y^2)/(xy^2)
=2y/(xy^2)
=2/(xy)
=2/(√2+1)(√2-1)
=2 .
y=√2-1
解:【1/(x-y)】-【1/(x+y)】/【xy²/(x²-y²)】
=(x+y-x+y)/(x^2-y^2)*(x^2-y^2)/(xy^2)
=2y/(xy^2)
=2/(xy)
=2/(√2+1)(√2-1)
=2 .
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解:【1/(x-y)】-【1/(x+y)】/【xy²/(x²-y²)】
=(x+y-x+y)/(x^2-y^2)*(x^2-y^2)/(xy^2)
这一步的(x+y-x+y)/(x^2-y^2)怎么来的,我怎么弄不出来
追答
x-y 、x+y 是分母,公分母是:x^2-y^2
1/(x-y)=(x+y)/(x^2-y^2)
1/(x+y)=(x-y)/(x^2-y^2)
1/(x-y)-1/(x+y)
=(x+y)/(x^2-y^2)-(x-y)/(x^2-y^2)
=(x+y-x+y)/(x^2-y^2)
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