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