(x)/(x+3)+(4x+6)/(x^2+4x+3)=0

x/(x + 3) + (4x + 6)/(x² + 4x + 3) = 0

x/(x + 3) + (4x + 6)/(x + 3)*(x + 1) = 0

x + 3 ≠ 0 => x ≠ -3

x + 1 ≠ 0 => x ≠ -1

x*(x + 1)/(x + 1)*(x + 3) + (4x + 6)/(x + 1)*(x + 3) = 0

(x² + x + 4x + 6)/(x + 1)*(x + 3) = 0 =>

=> x² + 5x + 6 = 0, x ≠ -3, x ≠ -1

x² + 5x + 6 = 0 => x₁*x₂ = 6, x₁ + x₂ = -5 =>

=> x₁ = -2, x₂ = -3.

Корень x₂ = -3 не подходит.

Единственное решение x = -2.

Ответ: x = -2.