已知a-b/b=1/2求3a^2-5ab+2b^2/2a^2+3ab-5b^2的值

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已知a-b/b=1/2求3a^2-5ab+2b^2/2a^2+3ab-5b^2的值
已知a-b/b=1/2求3a^2-5ab+2b^2/2a^2+3ab-5b^2的值

已知a-b/b=1/2求3a^2-5ab+2b^2/2a^2+3ab-5b^2的值
(a-b)/b=1/2
a-b=b/2
a=3b/2
(3a^2-5ab+2b^2)/(2a^2+3ab-5b^2)
=(a-b)(3a-2b)/[ (a-b)(2a+5b) ]
=(3a-2b)/(2a+5b)
代入a=3b/2
(5b/2)/8b
=5/16

(a-b)/b=1/2
a-b=b/2
所以
(3a^2-5ab+2b^2)/(2a^2+3ab-5b^2)
=(a-b)(3a-2b)/[ (a-b)(2a+5b) ]
=(3a-2b)/(2a+5b)
=(3a-3b+b)/(2a-2b+7b)
=(5b/2)/(8b)
=(5/2)/8
=5/16