How do you solve ((3x-2)(x-4))/(x+4)^2<0 using a sign chart?

1 Answer
Jan 13, 2017

The answer is =x in ] 2/3 , 4 [

Explanation:

Let f(x)=((3x-2)(x-4))/(x+4)^2

The domain of f(x) is D_f(x)=RR-{-4}

The denominator is >0, AA x in D_f(x)

Let's do the sign chart

color(white)(aaaa)xcolor(white)(aaaa)-oocolor(white)(aaaa)-4color(white)(aaaa)2/3color(white)(aaaaaa)4color(white)(aaaa)+oo

color(white)(aaaa)3x-2color(white)(aaaa)-color(white)(aa)color(red)(∥)color(white)(a)-color(white)(aaaa)+color(white)(aaaa)+

color(white)(aaaa)3x-2color(white)(aaaa)-color(white)(aa)color(red)(∥)color(white)(a)-color(white)(aaaa)-color(white)(aaaa)+

color(white)(aaaa)f(x)color(white)(aaaaaa)+color(white)(aa)color(red)(∥)color(white)(a)+color(white)(aaaa)-color(white)(aaaa)+

Therefore,

f(x)<0, when x in ] 2/3 , 4 [