Question

Tìm x £ Z

2x-1:x+3

Answer 1

\(2x-1⋮x+3\)

\(\Leftrightarrow\) \(2\left(x+3\right)-4⋮x+3\)

\(\Rightarrow\) \(4⋮x+3\)

\(\Rightarrow\)\(x+3\inƯ\left(4\right)\)

\(\text{Ta có}\) \(Ư\left(4\right)=\left(-1;-2;-4;1;2;4\right)\)

\(\text{*Nếu x + 3 = -1}\)

\(\Rightarrow x=-4\)

\(\text{*Nếu x + 3 = -2}\)

\(\Rightarrow x=-5\)
\(\text{*Nếu x + 3 = -4 }\)

\(\Rightarrow x=-7\)
\(\text{*Nếu x + 3 = 1 }\)

\(\Rightarrow x=-2\)

\(\text{*Nếu x + 3 = 2}\)

\(\Rightarrow x=-1\)

\(\text{*Nếu x + 3 = 4}\)

\(\Rightarrow x=1\)

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

Answer 2

2x-1\(⋮\)x+3

2x+6-7\(⋮\)x+3

2(x+3)-7\(⋮\)x+3

Vì 2(x+3)\(⋮\)x+3

buộc 7\(⋮\)x+3=>x+3\(\in\)Ư(7)={1;7;-1;-7}

Với x+3=1=>x= -2

x+3=7=>x=4

x+3= -1=>x= -4

x+3= -7=>x= -10

Vậy x\(\in\){-2;4;-4;-10}