`C=(4x-6)/(2x+1)=(4x+2-8)/(2x+1)=(2(2x+1)-8)/(2x+1)=2-8/(2x+1)` ĐK:`x\ne-1/2`
Để `C` có giá trị nguyên
`=> 8/(2x+1)` nguyên
`=> 8 \vdots 2x+1`
Do `x` nguyên
`=> 2x+1\inƯ(8)={+-1;+-2;+-4;+-8}`
`=> 2x\in{0;-2;1;-3;3;-5;7;-9}`
`=> x\in{0;-1} (\text{tm})`
Vậy `x\in{0;-1}`
Đáp án + Giải thích các bước giải:
`C=(4x-6)/(2x+1)`
`=(2(2x+1)-8)/(2x+1)`
`=2-(8)/(2x+1)`
Để biểu thức `C` có giá trị nguyên
`->(8)/(2x+1)∈ZZ`
`->8\vdots 2x+1`
`->2x+1∈Ư(8)={±1;±2;±4;±8}`
Với `x` nguyên `->2x+1` là số lẻ
`->2x+1∈{+-1}`
Lập bảng giá trị :
$\begin{array}{|c|c|}\hline 2x+1&-1&1\\\hline x&-1&0\\\hline\end{array}$
Với `x=-1->C=(4.(-1)-6)/(2.(-1)+1)=(-10)/(-1)=10`
Với `x=0->C=(4.0-6)/(2.0+1)=(-6)/(1)=-6`
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