How do you solve \frac { x - 8} { x - 4} > 0?
2 Answers
Here manuplate th numerator to relate with denominator,
now seprating numerator
thus,
hence
to satisfy the above question
Explanation:
"the zeros of the numerator/denominator are"
"numerator "x=8," denominator "x=4
"these indicate where the rational function may change"
"sign"
"the intervals on the domain are"
x<4,color(white)(x)4 < x <8,color(white)(x)x>8
"consider a "color(blue)"test point " "in each interval"
"we want to find where the function is positive " >0
"substitute each test point into the function and consider"
"its sign"
color(magenta)"x = 3"to(-)/(-)tocolor(red)" positive"
color(magenta)"x=5"to(-)/(+)tocolor(blue)" negative"
color(magenta)"x = 10"to(+)/(+)tocolor(red)" positive"
rArr(-oo,4)uu(8,+oo)" is the solution"
graph{(x-8)/(x-4) [-10, 10, -5, 5]}