Mathematics: Solve x+2/x-4 0 a)–4 x –2 b)–2 x 4 c)–2 x –4

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Solve x+2/x-4 0 a)–4 x –2 b)–2 x 4 c)–2 x –4

matt199296

10.03.2022

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

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

B) -2 < x < 4
Solve x+2/x-4< 0 a)–4 < x < –2 b)–2 < x < 4 c)–2 < x < –4

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