Question

b) tìm số nguyên x để phân số \(\frac{2x-1}{x+3}\)là số nguyên

Answer 1

2x-1/x+3=x/x+3 + x-1/x+3

Answer 2

\(\frac{2x-1}{x+3}\)\(=\frac{2\left(x+3\right)-7}{x+3}\)\(=2-\frac{7}{x+3}\)\(\Rightarrow x+3\in U\left(7\right)\)

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Answer 3

\(\frac{2x-1}{x+3}\inℤ\Leftrightarrow2x-1⋮x+3\)

\(\Rightarrow2x+6-7⋮x+3\)

\(\Rightarrow2\left(x+3\right)-7⋮x+3\)

      \(2\left(x+3\right)⋮x+3\)

\(\Rightarrow7⋮x+3\)

\(\Rightarrow x+3\inƯ\left(7\right)\)

     \(x\inℤ\Rightarrow x+3\inℤ\)

\(\Rightarrow x+3\in\left\{-1;1;-7;7\right\}\)

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