The number of common tangents to the circles $x^2+y^2-x=0,x^2+y^2+x=0$, is

The centres and radii of the circles are: 

Centres: $C_1(1/2,0)C_2(-1/2,0)$

Radii :    $r_1=\frac{1}{2}{r}_2=\frac{1}{2}$

Clearly $C_1{C}_2=r_1+r_2.$

Therefore, the circles touch each other externally. Hence, there are 3 common tangents