Question

Tìm x thuộc Z để A có giá trị nguyên: A= x+3/x-1.

Answer 1

Ta có: \(A=\dfrac{x+3}{x-1}=\dfrac{x-1+4}{x-1}=1+\dfrac{4}{x-1}\)

Để A có giá trị nguyên thì \(x-1\inƯ\left(4\right)\)

ta có:\(Ư\left(4\right)=\left\{\pm1,\pm2,\pm4\right\}\)

Ta có bảng sau:

x-1	-1	1	-2	2	-4	4
x	0	2	-1	3	-3	5

Vậy \(x\in\left\{-3,-1,0,2,3,5\right\}\)

=.= hok tốt!!

Answer 2

Answer 3

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

⇒ Để A có giá trị nguyên ⇒ \(x-1\)∈ \(Ư\left(4\right)\)

⇒ \(x-1\)∈ \(\left\{-4;-2;-1;1;2;4\right\}\)

TH1 \(x-1\)= -4

x = -3

TH2 \(x-1\)= -2

x = -1

TH3 \(x-1\)= -1

x = 0

TH4 \(x-1\)= 1

x = 2

TH5 \(x-1\)= 2

x = 3

TH6 \(x-1\)= 4

x = 5

Vậy x ∈ \(\left\{-3;-1;0;2;3;5\right\}\)

Answer 4

\(A=\dfrac{x+3}{x-1}=\dfrac{\left(x-1\right)+4}{x-1}=\dfrac{x-1}{x-1}+\dfrac{4}{x-1}=1+\dfrac{4}{x-1}\) (giải chi tiết cho bn dễ hiểu)

Để A có gt nguyên \(\Leftrightarrow x=\left(x-1\right)\inƯ\left(4\right)\)

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

\(\Rightarrow x\in\left\{-3;-2;-1;0;2;3;5\right\}\)