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【数学计算题】化简【x/(x²-2x+1)+1/(1-x)】÷2/(x²-1)

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【数学计算题】化简【x/(x²-2x+1)+1/(1-x)】÷2/(x²-1)
【数学计算题】
化简
【x/(x²-2x+1)+1/(1-x)】÷2/(x²-1)
因式分解
49(x-y)²-9(y+x)²
x^4-y^4
(x+y)²-16(x-y)²
【x/(x²-2x+1)+1/(1-x)】÷2/(x²-1)
﹦【x/(x-1)²-1/(x-1)】÷2/(x²-1)
﹦【x/(x-1)²-(x-1)/(x-1)²】÷2/(x²-1)
﹦【1/(x-1)²】×【(x²-1)/2】
﹦1/2

49(x-y)²-9(y+x)²
﹦【7(x-y)】²-【3(x+y)】²
﹦【7(x-y)+3(x+y)】【7(x-y)-3(x+y)】
﹦(10x-4y)(4x-10y)
﹦4(5x-2y)﹙2x-5y﹚

x^4-y^4
﹦﹙x²﹚²-﹙y²﹚²
﹦﹙x²+y²﹚﹙x²-y²﹚
﹦﹙x²+y²﹚﹙x+y﹚﹙x-y﹚

(x+y)²-16(x-y)²
﹦﹙x+y﹚²-【4﹙x-y﹚】²
﹦【(x+y﹚+4﹙x-y﹚】【﹙x+y﹚-4﹙x-y﹚】
﹦(5x-3y)(5y-3x)