Question

Tìm x sao cho 3x+1/2x+3 thuộc z

Answer 1

\(\frac{3x+1}{2x+3}\inℤ\Leftrightarrow3x+1⋮2x+3\)

\(\Rightarrow2\left(3x+1\right)⋮2x+3\)

\(\Rightarrow6x+2⋮2x+3\)

\(\Rightarrow6x+9-7⋮2x+3\)

\(\Rightarrow3\left(2x+3\right)-7⋮2x+3\)

     \(3\left(2x+3\right)⋮2x+3\)

\(\Rightarrow7⋮2x+3\)

\(\Rightarrow2x+3\inƯ\left(7\right)=\left\{-1;1;-7;7\right\}\)

\(\Rightarrow2x\in\left\{-4;-2;-10;4\right\}\)

\(\Rightarrow x\in\left\{-2;-1;-5;2\right\}\)