Для упрощения данного выражения сначала найдем общий знаменатель для дробей в знаменателе:

Общий знаменатель: x(x + 1)(x - 1)

4x^2 + 2x + 6 = 4x^2 + 2x + 6

x^2 - 1 = (x - 1)(x + 1)

3/x - 1 + 2x/x + 1 = (3(x + 1) + 2x(x - 1)) / x(x + 1)

4x^2 + 2x + 6 / x^2 - 1 : (3/x - 1 + 2x/x + 1)
= (4x^2 + 2x + 6) / ((x - 1)(x + 1)) : [(3(x + 1) + 2x(x - 1)) / x(x + 1)]
= (4x^2 + 2x + 6) / ((x - 1)(x + 1)) (x(x + 1) / (3(x + 1) + 2x(x - 1)))
= [(4x^2 + 2x + 6) x(x + 1)] / [(x - 1)(x + 1) (3(x + 1) + 2x(x - 1))]
= [(4x^2 + 2x + 6) x(x + 1)] / [(x - 1)(x + 1) (3x + 3 + 2x^2 - 2x)]
= [(4x^2 + 2x + 6) x(x + 1)] / [(x - 1)(x + 1) * (2x^2 + x + 3)]
= [4x^3 + 2x^2 + 6x] / [(x^2 - 1)(2x^2 + x + 3)]
= [4x^3 + 2x^2 + 6x] / [(x^2 - 1)(2x^2 + x + 3)]
= x(4x^2 + 2x + 6) / [(x^2 - 1)(2x^2 + x + 3)]
= x(4x^2 + 2x + 6) / [(x^2 - 1)(2x^2 + x + 3)]
= x(4x^2 + 2x + 6) / [(x + 1)(x - 1)(2x^2 + x + 3)]
= x(4x^2 + 2x + 6) / [(x + 1)(x - 1)(2x^2 + x + 3)]