Question

giải bất phương trình;

a) (x+1)*(x-2)>0

b) (x+1)/(x-3)<0

Answer 1

a)Vì \(\left(x+1\right)\left(x-2\right)>0\)

Suy ra \(x+1;x-2\) cùng dấu

Xét \(\left\{{}\begin{matrix}x+1>0\\x-2>0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x>-1\\x>2\end{matrix}\right.\)

Xét \(\left\{{}\begin{matrix}x+1< 0\\x-2< 0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x< -1\\x< 2\end{matrix}\right.\)

b)\(\dfrac{x+1}{x-3}< 0\)

Suy ra \(x+1;x-3\) ngược dấu

Mà \(x+1>x-3\forall x\)

\(\Rightarrow\left\{{}\begin{matrix}x+1>0\\x-3< 0\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}x>-1\\x< 3\end{matrix}\right.\)