  We calculate the fully-differential rate of the decays $B\to P\tau(\to
\mu\bar\nu\nu)\bar\nu$ where $P = D,\pi$, which is a background to the
semimuonic decays $B\to P\mu\bar\nu$. The decays with a $3\nu$ final state can
have a sizeable impact on the experimental analyses of the ratios $R_D$ and
$R_\pi$, depending on the event selection in the analysis. We outline a
strategy which permits the extraction of $R_P \mathcal{B}(\tau \to
\mu\bar\nu\nu)$ from the neutrino-inclusive rate. Our analytic results can also
be used to test both existing and upcoming experimental analyses. We further
provide Monte Carlo samples of the 5D rate of the neutrino-inclusive decays
$B\to P\mu X_{\bar\nu}$.
