已知a-2b/b=1/2,求分式a^2+ab-2b^2/a^2-ab+2b^2的值

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(a-2b)/b=1/2
a/b-2=1/2
a/b=5/2
(a^2+ab-2b^2)/(a^2-ab+2b^2)
= (a+2b)(a-b) / {(a+b)(a-2b)
= (a/b+2)(a/b-1) / {a/b+1)(a/b-2)}
= (5/2+2)(5/2-1) / {5/2+1)(5/2-2)}
= (9/2)(3/2) / {7/2)(1/2)}
= 27/7

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