do đó \(\left\{{}\begin{matrix}x+1=1\\x+1=2\\x+1=-2\\x=1=-1\end{matrix}\right.\)⇒ \(\left\{{}\begin{matrix}x=0\\x=1\\x=-3\\x=-2\end{matrix}\right.\)
vậy \(\left\{{}\begin{matrix}x=0\\x=1\\x=-3\\x=-2\end{matrix}\right.\)
Tìm giá trị nguyên của x để M nhận giá trị nguyên
M = \(\frac{2x}{x+1}\)= \(\frac{2\left(x+1\right)-2}{x+1}\)=\(\frac{2\left(x+1\right)}{x+1}\)-\(\frac{2}{x+1}\)= 2-\(\frac{2}{x+1}\)
⇒ 2 ⋮ x+1 thì M là số nguyên
⇒x + 1 ∈ Ư(2) = { 1; -1; 2; -2}
Do đó: \(\left\{{}\begin{matrix}x+1=2\\x+2=2\\x+\left(-2\right)=2\\x+\left(-1\right)=2\end{matrix}\right.\)⇒ \(\left\{{}\begin{matrix}x=1\\x=0\\x=4\\x=3\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=1\\x=0\\x=4\\x=3\end{matrix}\right.\)
