How do you find lim (x+5)(1/(2x)+1/(x+2)) as x->1 using l'Hospital's Rule or otherwise?

${\lim}_{x \rightarrow 1} \left(x + 5\right) \left(\frac{1}{2 x} + \frac{1}{x + 2}\right) = 6 \left(\frac{1}{2} + \frac{1}{3}\right) = 3 + 2 = 5$