How do you solve $m/(m-5)+3/(m-1)>0$ using a sign chart?

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How do you solve $m/(m-5)+3/(m-1)>0$ using a sign chart?

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Answer 1 · 2017-04-11T19:47:57

The solution is $m in (-oo,-5)uu(1,3)uu(5,+oo)$

Explanation:

Let's do some simplification

$m/(m-5)+3/(m-1)>0$

$(m^2-m+3m-15)/((m-5)(m-1))>0$

$(m^2+2m-15)/((m-5)(m-1))>0$

$((m+5)(m-3))/((m-5)(m-1))>0$

Let $f(m)=((m+5)(m-3))/((m-5)(m-1))$

We can build the sign chart

$color(white)(aaaa)$ $m$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-5$ $color(white)(aaaaaaa)$ $1$ $color(white)(aaaaa)$ $3$ $color(white)(aaaaaaa)$ $5$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $m+5$ $color(white)(aaaa)$ $-$ $color(white)(aaaaa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $m-1$ $color(white)(aaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $m-3$ $color(white)(aaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aa)$ $+$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $m-5$ $color(white)(aaaa)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $-$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(m)$ $color(white)(aaaaa)$ $+$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$ $color(white)(aa)$ $-$ $color(white)(aaaa)$ $||$ $color(white)(aa)$ $+$

So,

$f(m)>0$ when $m in (-oo,-5)uu(1,3)uu(5,+oo)$

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How do you solve $m/(m-5)+3/(m-1)>0$ using a sign chart?

1 Answer

Explanation:

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How do you solve m/(m-5)+3/(m-1)>0m/(m-5)+3/(m-1)>0 using a sign chart?

1 Answer

Explanation:

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How do you solve $m/(m-5)+3/(m-1)>0$ using a sign chart?