Question

[(a^2-b^2)/ab]-(ab-b^2)/(ab-a^2) (有图)

我算到(a+b+b^2-ab)/ab 就算不下去了。正确答案是a/b 但我希望得到过程

Answer 1

Answer 2

后面一个分母a(a-b)
通分，乘ab(a-b)得
原式=[(a^2-b^2)(b-a)-(ab-b^2)b]/[ab(b-a)]
=[-(a-b)^2(a+b)-(a-b)b^2]/[ab(a-b)]
=[(b-a)(a+b)-b^2]/(ab)
=a^2/(ab)
=a/b

Answer 3

解
(a²-b²)/ab-(ab-b²)/(ab-a²)
=(a²-b²)/ab-b(a-b)/a(b-a)
=(a²-b²)/ab+b(a-b)/a(a-b)
=(a²-b²)/ab+b/a
=(a²-b²)/ab+b²/ab
=(a²-b²+b²)/ab
=a²/ab
=a/b

Answer 4

=(a²-b²)/ab +b(a-b)/a(a-b)
=(a²-b²)/ab+b/a
=(a²-b²)/ab+b²/ab
=(a²-b²+b²)/ab
=a²/ab
=a/b