Answer:
[tex]★\:\: \frac{3 {x}^{3} - 18 {x}^{2} + 27x}{2 {x}^{2} + 2x - 12}\:when\:x≠2,\:3 \\ = \frac{3x( {x}^{2} - 6x + 9) }{2( {x}^{2} + x - 6) } \\ = \frac{3x( {(x)}^{2} - 2 \times (3) \times (x) + {(3)}^{2} ) }{2( {x}^{2} + 3x - 2x - 6) } \\ = \frac{3x {(x - 3)}(x - 3) }{2(x(x + 3) - 2(x + 3))} \\ = \boxed{‡ \frac{3x {(x - 3)}^{2} }{2(x + 3)(x - 2)}‡}✓[/tex]
3x(x-3)²/2(x+3)(x-2) is the right answer.
