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

1 Answer
Oct 14, 2017

Answer:

The solution is #a in (-oo,0) uu (1,+oo)#

Explanation:

Let #f(a)=(a-1)/a#

The sign chart is

#color(white)(aaaa)##a##color(white)(aaaa)##-oo##color(white)(aaaaaaaa)##0##color(white)(aaaaaaaa)##1##color(white)(aaaa)##+oo#

#color(white)(aaaa)##a##color(white)(aaaaaaaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##a-1##color(white)(aaaaaa)##-##color(white)(aaaa)####color(white)(aaaaa)##-##color(white)(aaaa)##+#

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

Therefore,

#f(a)>0#, when #a in (-oo,0) uu (1,+oo)#

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