How do you solve #(x+3)^2/x<=0# using a sign chart?

1 Answer
Jan 15, 2017

Answer:

The answer is #x in ] -oo,0 [#

Explanation:

Let #f(x)=(x+3)^2/x#

The domain of #f(x)# is #D_f(x)=RR-{0}#

#AAx in D_f(x), (x+3)^2>0#

We can make the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaaa)##0##color(white)(aaaaa)##+oo#

#color(white)(aaaa)##x##color(white)(aaaaaaaa)##-##color(white)(aaaa)##color(red)(∥)##color(white)(a)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##-##color(white)(aaa)##color(red)(∥)##color(white)(a)##+#

Therefore,

#f(x)<=0# when #x in ] -oo,0 [#