When we take an open D chord (D-F♯-A) and we add the open A to the chord, we would have second inversion as A is the fifth in the chord. The chord would be noted as D/A.
If we were to add the 2nd fret on the low E to the chord (which is an F♯ note), and still mute the open A, we would have first inversion as F♯ is the third in the chord. This would be noted D/F♯.
Now, if we play first inversion, and add in the open A, how would we notate that? The chord would still be a D chord as we only still just have the notes D, F♯, and A. It would still be first inversion as the third, or F♯, is still the bass note. The curveball here is that there is now a fifth (A) between the bass note and the root of the chord. How do we show this?