Question

已知a/a-b=2,求a^3-4a^2b-5ab^2/a^3-6a^2b+5ab^2的值

已知a/a-b=2,求a^3-4a^2b-5ab^2/a^3-6a^2b+5ab^2的值

Answer 1

a/(a-b)=2 倒数 (a-b)/a=1/2 1-b/a=1/2 b/a=1/2
(a^3-4a^2b-5ab^2)/(a^3-6a^2b+5ab^2)
上下同除以a^3
原式=(1-4b/a-5(b/a)^2)/(1-6b/a+5(b/a)^2)
=(1-2-5/4)/(1-3+4/5)=3

Answer 2

a/a-b = 2 所以 a = 2b
a^3-4a^2b-5ab^2/a^3-6a^2b+5ab^2
=a(a^2 - 4ab - 5b^2)/a(a^2 - 6ab + 5b^2)
=(a - 5b)(a +b)/(a - 5b)(a - b)
= a + b/a - b
=3b/b
=3