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

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Answer 1 · 2017-01-15T10:51:19

The answer is $x in ] -oo,0 [$

Let $f(x)=(x+3)^2/x$

The domain of $f(x)$ is $D_f(x)=RR-{0}$

$AAx in D_f(x), (x+3)^2>0$

We can make the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaaaa)$ $0$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaa)$ $x$ $color(white)(aaaaaaaa)$ $-$ $color(white)(aaaa)$ $color(red)(∥)$ $color(white)(a)$ $+$

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

Therefore,

$f(x)<=0$ when $x in ] -oo,0 [$

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