Question

Tìm x để \(\dfrac{2x+2}{x+3}\)nhận giá trị nguyên

Giúp mình với ạ mình cần gấp lắm rồi TT_TT

Answer 1

Để (2x+2)/(x+3) là số nguyên thì \(x+3\in\left\{1;-1;2;-2;4;-4\right\}\)

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

Answer 2

\(\dfrac{2x+2}{x+3}=\dfrac{2\left(x+3\right)-4}{x+3}=2-\dfrac{4}{x+3}\in Z\\ \Leftrightarrow x+3\inƯ\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\\ \Leftrightarrow x\in\left\{-7;-5;-4;-2;-1;1\right\}\)

Answer 3

\(\Rightarrow9⋮x+3\)

\(\Rightarrow x+3\in\left\{1;-1;3;-3;9;-9\right\}\)

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