Question

In the given problem, solve and graph.

Express answers in both inequality and interval notation.

$\frac{x^2+5x}{x-3}\ge 0$

Answer 1

$\frac{x^2+5x}{x-3}\ge 0$

$\frac{x(x+5)}{x-3}\ge 0$

	x<-5	x=-5	-5<x<0	x=0	0<x<3	x=3	x>3
x	-	-	-	0	+	+	+
x+5	-	0	+	+	+	+	+
x-3	-	-	-	-	-	0	+
$\frac{x(x+5)}{x-3}$	-	0	+	0	-	undefined	+

$-5\le x\le 0,x>3$

Interval notation $[-5,0]\cup (3,\infty )$