How do you solve #(x-6)/(x+1)>0#?

1 Answer
Apr 23, 2017

Answer:

#(-oo,-1)uu(6,+oo)#

Explanation:

#"the zero's of the numerator/denominator are"#

#"numerator"color(white)(x)x=6, "denominator"color(white)(x)x=-1#

These indicate where the rational function may change sign and which value x cannot be on the denominator.

#"the intervals for consideration are"#

#x < -1, -1 < x < 6, x>6#

#"Consider a "color(blue)"test point"" in each interval"#

#"we want to find where the function is positive, that is ">0#

#"substitute each test point into the function and consider it's sign"#

#color(red)(x=-2)to(-)/(-)tocolor(red)" positive"#

#color(red)(x=2)to(-)/(+)tocolor(blue)" negative"#

#color(red)(x=8)to(+)/(+)tocolor(red)" positive"#

#rArr(-oo,-1)uu(6,+oo)#
graph{(x-6)/(x+1) [-10, 10, -5, 5]}