Question

X2+4x+3/ x2+6x+9 simplificar e colocar os termos em evidencia

Answer 1

(x² + 4x + 3)/(x² + 6x + 9) =
(x + 1).(x + 3)/(x + 3)² =
(x + 1)/(x + 3)

x² + 4x + 3 = (a + b)(c + d) → (x + 1)(x + 3)
ac + ad + bc + bd = x² + 4x + 3
(ac) = x² → a = x; b = x
(ad + bc) = 4x → (xd + bx) = 4x → (d + b)x = 4x; d = 1; b = 3
(bd) = 3 → (1.3) = 3

x² + 6x + 9 → Trinômio quadrado perfeito (a + b)²
a² = x²; a = x
b² = 9; b = 3
2ab = 2.x.3 = 6x
(a + b)² → (x + 3)²