How do you solve $((x+3)(x+5))/(x+2)>=0$ ?

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How do you solve $((x+3)(x+5))/(x+2)>=0$ ?

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Answer 1 · 2017-03-17T07:35:26

The solution is $x in [-5,-3] uu]-2, +oo[$

Explanation:

We solve this inequality with a sign chart

Let $f(x)=((x+3)(x+5))/(x+2)$

The domain of $f(x)$ is $D_f(x)=RR-{-2}$

Let build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-5$ $color(white)(aaaa)$ $-3$ $color(white)(aaaaaa)$ $-2$ $color(white)(aaaaaaa)$ $+oo$

$color(white)(aaaa)$ $x+5$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x+3$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x+2$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aaaa)$ $+$

Therefore,

$f(x)>=0$ when $x in [-5,-3] uu]-2, +oo[$

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How do you solve $((x+3)(x+5))/(x+2)>=0$ ?

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How do you solve ((x+3)(x+5))/(x+2)>=0((x+3)(x+5))/(x+2)>=0?

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How do you solve $((x+3)(x+5))/(x+2)>=0$ ?