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化简(a-b)/(a^1/3-b^1/3)-(a+b)/(a^1/3+b^1/3)
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化简(a-b)/(a^1/3-b^1/3)-(a+b)/(a^1/3+b^1/3)
▼优质解答
答案和解析
设a^1/3=m,b^1/3=n,则a=m^3,b=n^3
(a-b)/(a^1/3-b^1/3)-(a+b)/(a^1/3+b^1/3)
=(m^3-n^3)/(m-n)-(m^3+n^3)/(m+n)
=m^2+n^2+mn-(m^2+n^2-mn)
=2mn
=2(ab)^1/3
(a-b)/(a^1/3-b^1/3)-(a+b)/(a^1/3+b^1/3)
=(m^3-n^3)/(m-n)-(m^3+n^3)/(m+n)
=m^2+n^2+mn-(m^2+n^2-mn)
=2mn
=2(ab)^1/3
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