Question

In the given problem, solve and graph. Express the answer in both inequality and interval notation. $\frac{2}{x+1}\ge \frac{1}{x-2}$

Answer 1

$\frac{2}{x+1}\ge \frac{1}{x-2}$

$\frac{2}{x+1}-\frac{1}{x-2}\ge 0$

$\frac{x-5}{(x+1)(x-2)}\ge 0$

	x<-1	x=- 1	- 1<x<2	x=2	2<x<5	x=5	x>5
x-5	-	-	-	-	-	0	+
x-2	-	-	-	0	+	+	+
x+1	-	0	+	+	+	+	+
$\frac{x-5}{(x+1)(x-2)}$	-	undefined	+	undefined	-	0	+

$\left[\begin{array}{cc}Solution:& -1<x<2orx\ge 5\\ IntervalNotation:& (-1,2)\cup [5,\infty )\end{array}\right]$