# Inequalities: Variable in Denominator both sides

• Aug 27th 2012, 10:49 AM
bajpaiapurva
Inequalities: Variable in Denominator both sides
Please tell me how this question will be solved

1/(x+2) > 3/(x-3)

answer: (-9/2, -2) U (3,+infinity)

Though i know the answer but i dont how how will get it

Thanx
• Aug 27th 2012, 11:20 AM
earboth
Re: Inequalities: Variable in Denominator both sides
Quote:

Originally Posted by bajpaiapurva
Please tell me how this question will be solved

1/(x+2) > 3/(x-3)

answer: (-9/2, -2) U (3,+infinity)

Though i know the answer but i dont how how will get it

Thanx

$\frac1{x+2}>\frac3{x-3}~\implies~\frac{x-3-3(x+2)}{(x+2)(x-3)}>0$

Examine when a fraction is greater than zero.

If + means positive (> 0) and - means negative (<0) you'll get the following cases:

$\frac{+}{+ \cdot +}~\vee~\frac{+}{- \cdot -} ~\vee~\frac{-}{+ \cdot -}~\vee~\frac{-}{- \cdot +}$

Each fraction describes 3 inequalities.
• Aug 27th 2012, 11:30 AM
Plato
Re: Inequalities: Variable in Denominator both sides
Quote:

Originally Posted by bajpaiapurva
Please tell me how this question will be solved
$\frac{1}{(x+2)} > \frac{3}{(x-3)}$

answer: $(-9/2, -2) \cup (3,\infty)$
Though i know the answer but i dont how how will get it
Thanx

That answer is incorrect. It includes $x=5$ which does not work.

The given answer works for $\frac{1}{(x+2)} < \frac{3}{(x-3)}$.

Please check the post.