Question

Simplifique a expressão:

(2x⁵ - 14x⁴ + 24x³) / (32x⁴ - 2x⁶)

Answer 1

$\frac{2x^5-14x^4+24x^3}{32x^4-2x^6} = \frac{2x^3(x^2-7x+12)}{2x^3(16x-x^3)} = \frac{x^2-7x+12}{16x-x^3}= \frac{(x - 3)\cdot(x-4)}{x\cdot(16-x^2)}\\ = \frac{(x - 3)\cdot(x-4)}{-x\cdot(x^2-16)}= \frac{(x - 3)\cdot(x-4)}{-x\cdot(x+4)\cdot(x-4)}= \frac{(x - 3)}{-x\cdot(x+4)}=\frac{x - 3}{-x^2 - 4x}$