a) Để A là số nguyên \(\Leftrightarrow\frac{4x-5}{x+1}\in Z\)
\(\Leftrightarrow4x-5⋮x+1\)
Ta có : \(x+1⋮x+1\Rightarrow4x+4⋮x+1\)
\(\Rightarrow4x-5-4x-4⋮x+1\)
\(\Rightarrow-9⋮x+1\Leftrightarrow x+1\inƯ\left(-9\right)=\left\{\pm1,\pm3,\pm9\right\}\)
\(\Rightarrow x\in\left\{-2,0,-4,2,-10,8\right\}\)
Vậy : \(x\in\left\{-2,0,-4,2,-10,8\right\}\)
b) Để A là số nguyên \(\Leftrightarrow\frac{7x-3}{2x+1}\in Z\)
\(\Leftrightarrow7x-3⋮2x+1\)
\(\Leftrightarrow14x-6⋮2x+1\)
\(\Leftrightarrow14x-6-14x-7⋮2x+1\)
\(\Leftrightarrow-13⋮2x+1\Leftrightarrow2x+1\inƯ\left(-13\right)=\left\{\pm1,\pm13\right\}\)
\(\Leftrightarrow2x\in\left\{-2,0,-14,12\right\}\)
\(\Leftrightarrow x\in\left\{-1,0,-7,-6\right\}\)
