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(x-2)^5/[-(x-2)^3]/(x^2-4)^2=?同底数幂的除法速速!还有化简[(x^2-2xy+y^2)^2-x^4+y^4]/(x^2-y^2)^2）
题目详情
(x-2)^5/[-(x-2)^3]/(x^2-4)^2=?
同底数幂的除法 速速!
还有 化简[(x^2-2xy+y^2)^2-x^4+y^4]/(x^2-y^2)^2 ）
同底数幂的除法 速速!
还有 化简[(x^2-2xy+y^2)^2-x^4+y^4]/(x^2-y^2)^2 ）
▼优质解答
答案和解析
(x-2)^5/[-(x-2)^3]/(x^2-4)^2
=-(x-2)^(5-3)/(x+2)^2(x-2)^2
=-(x-2)^2/(x+2)^2(x-2)^2
=-1/(x+2)^2
[(x^2-2xy+y^2)^2-x^4+y^4]/(x^2-y^2)^2
=[(x-y)^4-(x^2+y^2)(x^2-y^2)]/(x+y)^2(x-y)^2
=(x-y)[(x-y)^3-(x^2+y^2)(x+y)]/(x+y)^2(x-y)^2
=(x^3-3x^2y+3xy^2-y^3-x^3-x^2y-xy^2-y^3)/(x+y)^2(x-y)
=(-4x^2y+2xy^2-2y^3/(x+y)^2(x-y)
=-(x-2)^(5-3)/(x+2)^2(x-2)^2
=-(x-2)^2/(x+2)^2(x-2)^2
=-1/(x+2)^2
[(x^2-2xy+y^2)^2-x^4+y^4]/(x^2-y^2)^2
=[(x-y)^4-(x^2+y^2)(x^2-y^2)]/(x+y)^2(x-y)^2
=(x-y)[(x-y)^3-(x^2+y^2)(x+y)]/(x+y)^2(x-y)^2
=(x^3-3x^2y+3xy^2-y^3-x^3-x^2y-xy^2-y^3)/(x+y)^2(x-y)
=(-4x^2y+2xy^2-2y^3/(x+y)^2(x-y)
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