How do you solve $(x^2-4)/(3-x)>=0$ using a sign chart?

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How do you solve $(x^2-4)/(3-x)>=0$ using a sign chart?

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Answer 1 · 2016-11-19T15:23:45

The answer is $x in] -oo,-2 ] uu [2, 3[$

Explanation:

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

The domain is $D_f=RR-{3}$

Let's do the sign chart

$color(white)(aaaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaaa)$ $-2$ $color(white)(aaaaa)$ $2$ $color(white)(aaaaa)$ $3$ $color(white)(aaaaa)$ $+oo$

$color(white)(aaaaa)$ $x+2$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aaa)$ $+$

$color(white)(aaaaa)$ $x-2$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaa)$ $+$

$color(white)(aaaaa)$ $3-x$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aaa)$ $-$

$color(white)(aaaaa)$ $f(x)$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaa)$ $-$

Therefore, $f(x)>=0$

when $x in] -oo,-2 ] uu [2, 3[$

graph{(x^2-4)/(3-x) [-34.51, 30.44, -18.83, 13.64]}

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How do you solve $(x^2-4)/(3-x)>=0$ using a sign chart?

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

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Explanation:

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How do you solve $(x^2-4)/(3-x)>=0$ using a sign chart?