Remember that,

#color(blue)("Average speed "=("Total distance travelled")/("Total time taken")#

The total distance travelled is #color(green)(d#

Now, let's calculate the time using the formula

#color(brown)("Speed"=("Distance ")/("Time")#

When the body moves with velocities #v_1 and v_2#, they take time #t_1 and t_2# and cover distances of #2/5 d and 3/5 d#

So,

#rArrcolor(green)(v_1=(2/5 d)/(t_1),t_1=(2/5 d)/v_1#

#rArrcolor(green)(v_2=(3/5 d)/(t_2),t_2=(3/5 d)/v_2#

Now combine all the values

#rarr"Average speed"=(d)/((2/5 d)/(v_1)+(3/5 d)/v_2#

#rarrd/(((2/5 dv_2)+(3/5 dv_1))/(v_1v_2))#

#rarr(dv_1v_2)/(2/5 dv_2+3/5 dv_1)#

#rarr(canceldv_1v_2)/(canceld(2/5 v_2+3/5 v_1))#

#rarr(v_1v_2)/((2v_2+3v_1)/5)#

#color(blue)(rArr(5v_1v_2)/(3v_1+2v_2)#

Hope this helps!!! ☺