How do you solve #((x+7)(x-3))/(x-1)>=0#?

1 Answer
Feb 3, 2017

Answer:

The answer is #x in [-7,1 [ uu [3,+oo[#

Explanation:

Let #f(x)=((x+7)(x-3))/(x-1)#

The domain of #f(x)# is #D_f(x)=RR-{1}#

Now we can build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-7##color(white)(aaaaaaa)##1##color(white)(aaaaaa)##3##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##x+7##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aa)##+##color(white)(aaaa)##+#

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

#color(white)(aaaa)##x-3##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##||##color(white)(aa)##-##color(white)(aaaa)##+#

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

Therefore,

#f(x)>=0# when #x in [-7,1 [ uu [3,+oo[#