I was asked to resolve $\displaystyle \frac{2x+1}{(2x+6)(x^2+4)}$ into partial fractions. I got: $\displaystyle \frac{2x+1}{(2x+6)(x^2+4)} \equiv \frac{-11}{(13)(2x+6)}+\frac{11x+19}{(26)(x^2+4)}$. Is it right?
A correct approach would be:
$\displaystyle \frac{2x+1}{(2x+6)(x^{2}+4)} = \frac{2x+1}{(2x+6)} \cdot \frac{1}{x^{2}+4}$
$\displaystyle \frac{2x+1}{(2x+6)} \cdot \frac{1}{x^{2}+4} = \frac{1}{2} \cdot \frac{2x+1}{x+3} \cdot \frac{1}{x^{2}+4}$
here is a start, I haven't tried to solve it further.