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已知非零整数ab,满足ab=a-b则a/b+b/a-ab=?
题目详情
已知非零整数ab,满足ab=a-b则a/b+b/a-ab=?
▼优质解答
答案和解析
ab=a-b ab+b=a b=a/(a+1)
a/b+b/a-ab
=a+1+1/(a+1)-a^2/(a+1)
=[(a+1)^2+1-a^2]/(a+1)
=(2a+2)/(a+1)
=2
a/b+b/a-ab
=a+1+1/(a+1)-a^2/(a+1)
=[(a+1)^2+1-a^2]/(a+1)
=(2a+2)/(a+1)
=2
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