분수부등식

$\displaystyle 1 + \frac{k}{x - k} - \frac{1}{x - 1} \leq 0$ $\displaystyle \frac{( x - k ) ( x - 1 ) + k ( x - 1 ) - ( x - k )}{( x - k ) ( x - 1 )} \leq 0$ $\displaystyle \frac{x ^{2} - 2 x + k}{( x - k ) ( x - 1 )} \leq 0$ $\displaystyle \frac{( x - 1 ) ^{2} + k - 1}{( x - k ) ( x - 1 )} \leq 0$ $k - 1 \geq 0$이므로 $\therefore 1 < x < k$ $\therefore k = 5$