A car travels a distance of x with speed v 1 and then same distance x with speed v 2 in the same direction.…

Average velocity of car is:

$v_{\mathrm{avg}}=\frac{\text{Total displacement}}{\text{Total time}}$

As the car is travelling along a straight line without turning, the magnitude of total displacement is same as the distance covered. 

The time taken to cover the first half is $\frac{x}{v_1}$ and the time taken to cover the second half is $\frac{x}{v_2}$

$\therefore v_{\mathrm{avg}} = \frac{2x}{{\displaystyle \frac{x}{v_1}}+{\displaystyle \frac{x}{v_2}}}$

$\Rightarrow v_{\mathrm{avg}}=\frac{2x\left(v_1{v}_2\right)}{v_{1}x+v_{2}x}=\frac{2v_1{v}_2}{v_1+v_2}$