Question

tìm x để A là số nguyên:
Bt A=3(x-1)/x+1

Answer 1

Ta có: 

\(A=\dfrac{3\left(x-1\right)}{x+1}=\dfrac{3x-3}{x+1}\)

\(A=\dfrac{3x+3-6}{x+1}=\dfrac{3\left(x+1\right)-6}{x+1}=3-\dfrac{6}{x+1}\)

Giá trị của A nguyên khi \(\dfrac{6}{x+1}\) nguyên

\(\Rightarrow6\) ⋮ \(x+1\Rightarrow x+1\inƯ\left(6\right)=\left\{1;-1;2;-2;3;-3;6;-6\right\}\)

\(\Rightarrow x\in\left\{0;-2;1;-3;2;-4;5;-7\right\}\)