= Solution
The first <Baumslag-Solitar group> is
$$
\langle a,b\mid bab^{-1}=a^{-1}\rangle\cong\mathbb Z\rtimes\mathbb Z,
$$
where the second <infinite cyclic group> acts on the first by inversion. The <presentation of a semidirect product> proves this identification; both copies of $\mathbb Z$ are <residually finite groups>, since reduction modulo a suitable positive integer separates any nonzero integer. The normal factor is finitely generated, so the <residual finiteness of semidirect products> theorem applies. \b[$\boxed{BS(1,-1)\text{ is residually finite}.}$]
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