已知a/2=b/3≠0,求代数式5a-2b/a^2-4b^2·(a-2b)的值

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已知a/2=b/3≠0,求代数式5a-2b/a^2-4b^2·(a-2b)的值
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已知a/2=b/3≠0,求代数式5a-2b/a^2-4b^2·(a-2b)的值
已知a/2=b/3≠0,求代数式5a-2b/a^2-4b^2·(a-2b)的值

已知a/2=b/3≠0,求代数式5a-2b/a^2-4b^2·(a-2b)的值
∵a/2=b/3
∴a=2b/3
则,5a-2b/a²-4b²(a-2b)
=(5a-2b)/(a+2b)(a-2b)×(a-2b)
=(5a-2b)/(a+2b)
=(10b/3-2b)/(2b/3+2b)
=(4b/3)/(8b/3)

a/2=b/3≠0,即3A=2b, A=2B/3
5a-2b/a^2-4b^2·(a-2b)=5a-2b/(a+2b)(a-2b) · (a-2b)
=(10b/3 - 2b )/(2b/3+2b)
=1/2

已知a/2=b/3≠0
所以a=2b/3
5a-2b/a^2-4b^2·(a-2b)
=(10b/3-2b)/[(4/9-4)b^2]·(2b/3-2b)
=(4b/3)/(-32/9b^2)·(-4b/3)
=1/2