Question

ìm x thuộc z để a có giá trị nguyên a=2x-3/x+2

Answer 1

\(A=\frac{2x-3}{x+2}=\frac{2x+4-7}{x+2}=\frac{2\left(x+2\right)-7}{x+2}=2-\frac{7}{x+2}\)

Để \(A\in Z\Leftrightarrow x+2\inƯ\left(7\right)=\left\{\pm1;\pm7\right\}\)

Ta có bảng: 

x+2	1	-1	7	-7
x	-1	-3	5	-9

Vậy...

Answer 2

\(A=\frac{2x-3}{x+2}=\frac{2x+4-7}{x+2}=\frac{2\left(x+2\right)-7}{x+2}=2+\frac{-7}{\left(x+2\right)}\)

Mà 2 \(\in Z\Rightarrow\frac{-7}{\left(x+2\right)}\in Z\)

\(\Rightarrow x+2\inƯ\left(-7\right)\)

\(\Rightarrow x+2\in\left\{1;-1;7;-7\right\}\)

Ta có bảng giá trị:

x+2	1	-1	7	-7
x	-1	-3	5	-9
	C	C	C	C

Vậy x \(\in:\left\{-1;-3;5;-9\right\}\)