Question

Cho P=\(\dfrac{4x}{x-3}\)

Tìm số nguyên x để biểu thức P xác định cũng là số nguyên

Answer 1

ĐKXĐ: \(x\ne3\)

Để \(P=\dfrac{4x}{x-3}\) nguyên \(\Leftrightarrow4x⋮x-3\)

\(\Rightarrow\left(4x-12\right)+12⋮x-3\)

\(\Rightarrow4\left(x-3\right)+12⋮x-3\)

\(\Rightarrow12⋮x-3\)

\(\Rightarrow x-3\in U\left(12\right)=\left\{-1;1;-2;2;-3;3;-4;4;-6;6;-12;12\right\}\)

\(\Rightarrow x\in\left\{2;4;1;5;0;6;-1;7;-3;9;-9;15\right\}\)

Vậy \(x\in\left\{2;4;1;5;0;6;-1;7;-3;9;-9;15\right\}\) thì \(P=\dfrac{4x}{x-3}\) nguyên