분수부등식 정수해

$f ( x ) = a ( x - 1 ) ( x - 5 )$ (단, $a > 0$), $f ( x ) - g ( x ) = h ( x ) = b ( x - 3 ) ( x + 3 )$(단, $b > 0$)라 하면 $\displaystyle \frac{g ( x )}{f ( x )} \geq 1$에서 $\displaystyle \frac{f ( x ) - h ( x )}{f ( x )} \geq 1$, $\displaystyle \frac{h ( x )}{f ( x )} \leq 0$, $\displaystyle \frac{b ( x - 3 ) ( x + 3 )}{a ( x - 1 ) ( x - 5 )} \leq 0$, $\displaystyle \frac{( x - 3 ) ( x + 3 )}{( x - 1 ) ( x - 5 )} \leq 0$, $( x + 3 ) ( x - 1 ) ( x - 3 ) ( x - 5 ) \leq 0$ $( x \neq 1 , x \neq 5 )$ $\therefore - 3 \leq x < 1$, $3 \leq x < 5$ $\therefore - 3 , - 2 , - 1 , 0 , 3 , 4$로 $6$개다.