How do you solve #a/(a+2)>0# using a sign chart?

1 Answer
Jan 13, 2017

Answer:

The answer is #a in ] -oo,-2 [uu ] 0, +oo [#

Explanation:

Let #f(a)=a/(a+2)#

The domain of #f(a)# is #D_f(a)=RR-{-2}#

Let's do the sign chart

#color(white)(aaaa)##a##color(white)(aaaaaaa)##oo##color(white)(aaaa)##-2##color(white)(aaaaaa)##0##color(white)(aaaa)##+oo#

#color(white)(aaaa)##a+2##color(white)(aaaaaa)##-##color(white)(aa)##color(red)(∥)##color(white)(aaa)##+##color(white)(aaa)##+#

#color(white)(aaaa)##a##color(white)(aaaaaaaaaa)##-##color(white)(aa)##color(red)(∥)##color(white)(aaa)##-##color(white)(aaa)##+#

#color(white)(aaaa)##f(a)##color(white)(aaaaaaa)##+##color(white)(aa)##color(red)(∥)##color(white)(aaa)##-##color(white)(aaa)##+#

Therefore,

#f(a)>0# when #a in ] -oo,-2 [uu ] 0, +oo [#