A vehicle travels half the distance L with speed $v_1$  and the other half with speed  $v_2$, then its average speed is 

Time taken to travel first half distance
$t_1=\frac{L/2}{v_1}=\frac{L}{2v_1}$
Time taken to travel second half distance,
$t_2=\frac{L/2}{v_2}=\frac{L}{2v_2}$
Total time taken $=t_1+t_2=\frac{L}{2v_1}+\frac{L}{2v_2}$
Average speed = $\frac{Totaldis\tan cetravelled}{Total\text{\hspace{0.33em}}timetaken}$
$=\frac{L}{\frac{L}{2v_1}+\frac{L}{2v_2}}=\frac{1}{\frac{1}{2}\left[\frac{1}{v_1}+\frac{1}{v_2}\right]}=\frac{2v_1{v}_2}{v_2+v_1}$