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comedy数学题目额化简：（x^4-y^4）/（2x^2+xy-y^2）×（2x-y）/（xy-y^2）÷(x^2+y^2/2)^2
题目详情
comedy数学题目额
化简：（x^4-y^4）/（2x^2+xy-y^2）×（2x-y）/（xy-y^2）÷(x^2+y^2/2)^2
化简：（x^4-y^4）/（2x^2+xy-y^2）×（2x-y）/（xy-y^2）÷(x^2+y^2/2)^2
▼优质解答
答案和解析
原式=[(x²+y²)(x+y)(x-y)/(2x-y)(x+y)]×[(2x-y)/y(x-y)]÷[(x²+y²)²/4]
=[(x²+y²)(x-y)/(2x-y)]×[(2x-y)/y(x-y)]×[4/(x²+y²)²]
=4(x²+y²)(x-y)(2x-y)/[(2x-y)y(x-y)(x²+y²)²]
=4/[y(x²+y²)]
=[(x²+y²)(x-y)/(2x-y)]×[(2x-y)/y(x-y)]×[4/(x²+y²)²]
=4(x²+y²)(x-y)(2x-y)/[(2x-y)y(x-y)(x²+y²)²]
=4/[y(x²+y²)]
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