Question

Cho A=2(x+1)/x+3

Tìm giá trị nguyên của x để biểu thức A có giá trị nguyên

Giúp mik với nhanh nhé

Answer 1

A∈Z⇒\(\dfrac{2\left(x+1\right)}{x+3}\in Z\Rightarrow\left(2x+2\right)⋮\left(x+3\right)\)

\(\Rightarrow\left(2x+6-4\right)⋮\left(x+3\right)\\ \Rightarrow\left[2\left(x+3\right)-4\right]⋮\left(x+3\right)\)

 \(\text{Mà}2\left(x+3\right)⋮\left(x+3\right)\\ \Rightarrow-4⋮\left(x+3\right)\\ \Rightarrow x+3\inƯ\left(-4\right)=\left\{-4;-2;-1;1;2;4\right\}\\ \Rightarrow x\in\left\{-7;-5;-4;-2;-1;1\right\}\)

 

Answer 2

- Bạn ơi lớp 6 cũng làm được nhé :)

x ∈{0;-6;-2;-4}

Answer 3

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

Để A nguyên \(\Rightarrow\dfrac{4}{x+3}\) nguyên

\(\Rightarrow x+3=Ư\left(4\right)=\left\{-4;-2;-1;1;2;4\right\}\)

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