Ta có : \(x-2\) là ước của \(3x+5\)

\(\Rightarrow3x+5⋮x-2\)

\(\Rightarrow3x-6+11⋮x-2\)

\(\Rightarrow3\left(x-2\right)+11⋮x-2\)

\(\Rightarrow11⋮x-2\)

\(\Rightarrow x-2\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)

\(\Rightarrow x\in\left\{1;3;-9;13\right\}\)

Vậy \(x\in\left\{1;3;-9;13\right\}\)

x - 2 là ước của 3x + 5

=> \(3x+5⋮x-2\)

=> \(3\left(x-2\right)-1⋮x-2\)

=> \(1⋮x-2\)

=> \(\orbr{\begin{cases}x-2=1\\x-2=-1\end{cases}}\)

=> \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)

Nhầm nhá ... mình sửa lại tí

=> \(3\left(x-2\right)+11⋮x-2\)

=> \(11⋮x-2\)

Còn lại tương tự bạn Huyền 

=> 3x+5 chia hết x-2

=>3(x-2) chia hết x-2

(3x+5) - 3(x-2) chia hết cho x-2

=>7 chia hết cho x-2

=>x-2 thuộc Ư(7)

TH1: x-2= 1

=>x = 3

TH2: x-2=-1

=> x = 1

TH3: x-2=7
=> x = 9              LOẠI

TH4:x-2=-7
=> x = -5             LOẠI

VẬY x = { 3; 1}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              =)))                                                                                                                                                                                         

    x − 2 là ước của 3x + 5

⇒ 3x + 5 ⋮ x − 2

⇒ 3x − 6 + 11 ⋮ x − 2

⇒ 3(x − 2) + 11 ⋮ x − 2

⇒ 11 ⋮ x − 2

⇒ x − 2 ∈ Ư (11)

⇒ x − 2 ∈ { + 1 ; + 11 }

⇒ x ∈ { 1 ; 3 ;  − 9 ; 13 }

Vậy x ∈ { 1 ; 3 ; − 9 ; 13 }