How do you solve #(x-6)/(x+1)>0#?
1 Answer
Apr 23, 2017
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]}
