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

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- Aug 27th 2012, 09:49 AMbajpaiapurvaInequalities: 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, 10:20 AMearbothRe: Inequalities: Variable in Denominator both sides
$\displaystyle \frac1{x+2}>\frac3{x-3}~\implies~\frac{x-3-3(x+2)}{(x+2)(x-3)}>0$

Examine when a fraction is greater than zero.

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

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

Each fraction describes 3 inequalities. - Aug 27th 2012, 10:30 AMPlatoRe: Inequalities: Variable in Denominator both sides