Question

Solve x+2/x-4<0 A)–4 < x < –2 B)–2 < x < 4 C)–2 < x < –4

Answer 1

$Domain:\ x\neq-2\\\\\dfrac{x+2}{x-4}$

Other method:

$\dfrac{x+2}{x-4}$

zeros of numerator and denominator are x = -2 and x = 4.

Look at the second picture.

for x < -2 → x + 2 < 0 and x - 4 < 0

therefore $\dfrac{x + 2}{x - 4}=\dfrac{(-)}{(-)}>0$

for -2 < x < 4 → x + 2 > 0 and x - 4 < 0

therefore $\dfrac{x+2}{x-4}=\dfrac{(+)}{(-)} < 0$

for x > 4 → x + 2 > 0 and x - 4 > 0

therefore $\dfrac{x+2}{x-4}=\dfrac{(+)}{(+)} > 0$

Answer: B) -2 < x < 4