How do you solve #(x+3)/(x-1)>=0# using a sign chart?

1 Answer
Feb 13, 2018

Answer:

The solution is #x in (-oo,-3] uu(1,+oo)#

Explanation:

Let #f(x)=(x+3)/(x-1)#

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaa)##-3##color(white)(aaaaaaa)##1##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x+3##color(white)(aaaaa)##-##color(white)(aaa)##0##color(white)(aaa)##+##color(white)(aaaaa)##+#

#color(white)(aaaa)##x-1##color(white)(aaaaa)##-##color(white)(aaa)####color(white)(aaaa)##-##color(white)(aa)##||##color(white)(aa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaa)##0##color(white)(aaa)##-##color(white)(aa)##||##color(white)(aa)##+#

Therefore,

#f(x)>=0#, when #x in (-oo,-3] uu(1,+oo)#

graph{(x+3)/(x-1) [-16.02, 16.01, -8.01, 8.01]}