Find the partial fraction decomposition:

$$\dfrac{3x^2 - x + 4}{x^3 + 2x^2 + 6x}$$
\(\dfrac{\dfrac{2}{3}}{x} + \dfrac{\dfrac{7}{3}x - \dfrac{7}{3}}{x^2 + 2x + 6}\)

Find the partial fraction decomposition:

$$\dfrac{6x^2 + 21x + 11}{(x^2 + 3)(x + 5)}$$
\(\dfrac{4x + 1}{x^2 + 3} + \dfrac{2}{x + 5}\)

Find the partial fraction decomposition:

$$\dfrac{3x^2 + 5x - 4}{(x^2 - 7)(x + 1)}$$
\(\dfrac{2x + 3}{x^2 - 7} + \dfrac{1}{x + 1}\)