∴ a > 0, and 1 and 5 are two roots of the equation ax2-(a+ 1)x+b=0.

∴ 1+5 =-(A+ 1) A, and 1× 5 = B A,

The solution is a = 1.5, b= 1,

∴a+b= 65。

(2) if a≠0 and b= 1, then this inequality is AX2-(A+ 1) x+ 1 < 0,

∴ (ax-1) (x-1)1,1A < 1, then the solution set of this inequality is {x |1a < x

② If a= 1, 1 A = 1, and the solution set of this inequality is ￠,

③ if 0 < a < 1, 1A > 1, then the solution set of this inequality is {x | 1 < x < 1A}.

④ If a < 0, 1a < 1+0, then the solution set of this inequality is {x | {x | x < 1a, or x > 1}.