Question

22. A forma simplificada da fração x³-2x²-9x+18, com
x ≠ 0, x ≠ 2 e x ≠ 3, é:                   ≈≈≈≈≈≈≈≈≈≈≈≈≈
                                                          x³-5x²+6x

Answer 1

$\frac{x^2-2x^2-9x+18}{x^3-5x^2+6x}=\frac{(x - 3) (x - 2) (x + 3)}{x(x-3)(x-2)}=\frac{x+3}{x}$

Answer 2

x³-2x²-9x+18 =x²*(x-2)-9(x-2) =(x-2)*(x²-9) = (x-2)*(x+3)*(x-3)

x³-5x²+6x =x*(x²-5x+6)

****************************************

x²-5x+6=0

x'=[5+√(25-24)]/2 =(5+1)/2=3

x''=[5-√(25-24)]/2 =(5-1)/2=2

x²-5x+6=(x-x')*(x-x'')=(x-3)*(x-2)

*****************************************

x³-5x²+6x =x*(x²-5x+6) =x * (x-3)*(x-2)

(x³-2x²-9x+18)         (x-2)*(x+3)*(x-3)

≈≈≈≈≈≈≈≈≈≈≈≈≈ =   ≈≈≈≈≈≈≈≈≈≈≈≈≈

x³-5x²+6x                 x * (x-3) *( x-2)

=(x+3)/x               ....            para x ≠ 0, x ≠ 2 e x ≠ 3