Question

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tim x\(\in\)z

(4x+1)\(⋮\)(2x+2)

Answer 1

[Nguyễn Phương Uyên]

\(4x+1⋮2x+2\)

\(\Rightarrow4x+4-3⋮2x+2\)

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

      \(2\left(2x+2\right)⋮2x+2\)

\(\Rightarrow3⋮2x+2\)

\(\Rightarrow2x+2\inƯ\left(3\right)\)

\(\Rightarrow2x+2\in\left\{-1;1;-3;3\right\}\)

\(\Rightarrow2x\in\left\{-3;-1;-5;1\right\}\) 

\(\Rightarrow x\in\left\{-1,5;-0,5;-2,5;0,5\right\}\) mà x thuộc Z

\(\Rightarrow x\in\varnothing\)

Answer 2

[Dương Lam Hàng]

\(\frac{4x+1}{2x+2}=\frac{2\left(2x+2\right)-3}{2x+2}=2-\frac{3}{2x+2}\)

\(\Rightarrow3⋮\left(2x+2\right)\Rightarrow2x+2\inƯ\left(3\right)=\left\{1;3;-1;-3\right\}\)

Nếu 2x+2=1 => 2x=-1 => x=-1/2

Nếu 2x+2=3 => 2x=1 => x=1/2

Nếu 2x+2=-1 => 2x=-3 => x=-3/2

Nếu 2x+2=-3 => 2x=-5 => x = -5/2

Vậy x = {-1/2 ; 1/2 ; -3/2 ; -5/2} thì 4x+1 chia hết cho 2x+2