solve the inequality. Express the solution using interval notation and graph the solution set on the real number line

Question

x-4/x^2-4 greater or equal to O

Answer 1

(x-4)/(x^2-4) >= 0

Either both top and bottom are positive, or both negative

x-4 > 0 if x > 4
x^2-4 > 0 if |x| > 2

only x > 4 satisfies both requirements

x-4 < 0 if x < 4
x^2 - 4 < 0 if |x| < 2

So, -2 < x < 2

Solution set: (-2,2)U(4,oo)