How do you solve \frac { x - 8} { x - 4} > 0?

2 Answers

Here manuplate th numerator to relate with denominator,
(x-4-4)/(x-8) ,
now seprating numerator
(x-4)/(x-4)-(4)/(x-4)>0
thus,
1-4/(x-4)>0
hence
1>4/(x-4)

(x-4)>4

x>8
to satisfy the above question

Jul 31, 2017

(-oo,4)uu(8,+oo)

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]}