Which expression is the correct partial fraction decomposition of $\frac{1}{5 \cdot 7}$?

$\frac{1}{2}\left(\frac{1}{5} - \frac{1}{7}\right)$

$2\left(\frac{1}{5} - \frac{1}{7}\right)$

What is the partial fraction decomposition of the expression $\frac{1}{(k+4)(k+6)}$?

$\frac{1}{k+4} - \frac{1}{k+6}$

$2\left(\frac{1}{k+4} - \frac{1}{k+6}\right)$

$\frac{1}{2}\left(\frac{1}{k+6} - \frac{1}{k+4}\right)$

$\frac{1}{2}\left(\frac{1}{k+4} - \frac{1}{k+6}\right)$