How do you solve #(x + 13) /( x - 2)>0#?

1 Answer
Apr 21, 2017

Answer:

The solution is #x in (-oo,-13) uu (2,+oo)#

Explanation:

We solve this inequality with a sign chart.

Let #f(x)=(x+13)/(x-2)#

We build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-13##color(white)(aaaaaaa)##2##color(white)(aaaaaaa)##+oo#

#color(white)(aaaa)##x+13##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##+#

#color(white)(aaaa)##x-2##color(white)(aaaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+#

Therefore,

#f(x)>0# when #x in (-oo,-13) uu (2,+oo)#