tentukan himpunan penyelesaian pertidaksamaan -2

jawab

x² -2x - 11 /(x +5)  <2   atau  x² -2x - 11/(x+5)  > - 2

(i)  (x² -2x - 11)/(x+5) < 2 
(x² -2x -11)/(x+5) - 2 < 0
{(x²-2x -11)-2(x+5)} /(x+5) < 0
(x² -2x-11-2x-10)(x+5) < 0
(x²-4x-21)(x+5) < 0
(x-7)(x+3)(x+5) < 0
x< - 5 , x  > - 3 , x < 7

(ii) (x²-2x -11)/(x+5) > -2
(x²-2x- 11)/(x+5)+ 2 > 0
{x²-2x -11 +2(x+5)} /(x+5) >0
{x²-2x-11+2x+10}/(x+5) > 0
(x² - 1)(x+5) >0
(x -1)(x+1)(x+5) > 0
x > - 5, x < -1, x > 1

HP (i) n (ii)
x < - 5, x > - 3, x < 7
x > - 5 , x < - 1 , x > 1

HP
-3 < x < 1 , 1 < x < 7