Răspuns:
Explicație pas cu pas:
(4x-1) / (x²+7x+6) < -1 <=>
(4x-1) / (x²+7x+6) + 1 < 0 <=>
(4x-1) / (x²+7x+6) + ˣ²⁺⁷ˣ⁺⁶⁾1 < 0 <=>
(x²+11x+5) / (x²+7x+6) < 0
x²+11x+5 = 0 => x₁,₂ = [(-11±√(121-20)]/2 = (-11±√101)/2
x₁ = (-11-√101)/2 ≈ -10,5
x₂ = (-11 +√101)/2 ≈ - 0,5
x²+7x+6 = x²+6x+x+6 = x(x+6)+(x+6) = (x+6)(x+1)
x²+7x+6 = 0 => x₁ = -6 ; x₂ = -1
x I -∞ x₁ -6 -1 x₂ +∞
x²+11x+5 I ++++++0-----------------------0+++++++++++
x²+7x+6 I+++++++++++0------------0++++++++++++++
(x²+11x+5)/(x²+7x+6) I ++++++0------I++++++++I---0+++++++++++
=> x ∈ ((-11-√101)/2 ; -6) ∪ (-1 ; (-11+√101)/2)
