Để A=\(\frac{8x+5}{2x+3}\)là số nguyên \(\Leftrightarrow\)\(8x+5⋮2x+3\)
Ta có: \(8x+5=(8x+12)+5-12=\left(8x+12\right)-7⋮2x+3\)
vì \(8x+12⋮2x+3\)nên \(7⋮2x+3\)\(\Rightarrow2x+3\inƯ\left(7\right)\Rightarrow2x+3\in\xi-7;-1;1;7\xi\Rightarrow2x\in\xi-10;-4;-2;4\xi\)\(\Rightarrow x\in\xi-5;-2;-1;2\xi\)