Solve the following inequalities over the real domain:
\( \frac{x+1}{x-2}\ge 0 \)
The expresssion is undefined for \(x=2\).
The solution is \(x\in (-\infty,-1\rangle \cup (2,\infty)\).
\( \frac{x-2}{2x-8}\ge 1 \)
The expression is undefined for \(2x-8=0\) or \(x=4\).
The solution is \(x\in (4{,}6\rangle\).
\( \frac{x+3}{x-1}\ge \frac{x+1}{x-5} \)
The expression is undefined for \(x=1\) or \(x=5\).
The solution is \(x\in(-\infty,1) \cup (5{,}7\rangle\).
\( \frac1{x+2}<\frac{x}{x-1} \)
The expression is undefined for \(x=-2\) or \(x=1\).
The solution is \(x\in(-\infty,-2)\cup(1,\infty)\).