\(x=\frac{2a-3}{a-1}=\frac{2\left(a-1\right)-1}{a-1}=2-\frac{1}{a-1}\)
Để x là số nguyên => \(\frac{1}{a-1}\)nguyên
=> \(1⋮a-1\)
=> \(a-1\inƯ\left(1\right)=\left\{\pm1\right\}\)
=> \(a=\left\{2;0\right\}\)
\(x=\frac{2a-3}{a-1}=\frac{2a-1-2}{a-1}=\frac{-2}{a-1}\)
\(\Rightarrow a-1\inƯ\left(-2\right)=\left\{\pm1;\pm2\right\}\)
a - 1 | 1 | -1 | 2 | -2 |
a | 2 | 0 | 3 | -1 |