计算:(1)8a/ a^2-b^2 +b/ ab+b^2 (2)(x+1)/(x^2-2x+1) -(x-1)/(x^2
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计算:(1)8a/ a^2-b^2 +b/ ab+b^2 (2)(x+1)/(x^2-2x+1) -(x-1)/(x^2-1)
(1)8a/ a^2-b^2 +b/ ab+b^2
=8a/(a+b)(a-b)+b/b(a+b)
=8a/(a+b)(a-b)+1/(a+b)
=(8a+a-b)/(a²-b²)
=(9a-b)/(a²-b²)
(2)(x+1)/(x^2-2x+1) -(x-1)/(x^2-1)
=(x+1)/(x-1)²-(x-1)/(x+1)(x-1)
=(x+1)/(x-1)²-1/(x+1)
=[(x+1)²-(x-1)²]/(x+1)(x-1)²
=4x/(x+1)(x-1)²
=8a/(a+b)(a-b)+b/b(a+b)
=8a/(a+b)(a-b)+1/(a+b)
=(8a+a-b)/(a²-b²)
=(9a-b)/(a²-b²)
(2)(x+1)/(x^2-2x+1) -(x-1)/(x^2-1)
=(x+1)/(x-1)²-(x-1)/(x+1)(x-1)
=(x+1)/(x-1)²-1/(x+1)
=[(x+1)²-(x-1)²]/(x+1)(x-1)²
=4x/(x+1)(x-1)²
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