  The parallel sum for adjoinable operators on Hilbert $C^*$-modules is
introduced and studied. Some results known for matrices and bounded linear
operators on Hilbert spaces are generalized to the case of adjointable
operators on Hilbert $C^*$-modules. It is shown that there exist a Hilbert
$C^*$-module $H$ and two positive operators $A, B\in\mathcal{L}(H)$ such that
the operator equation $A^{1/2}=(A+B)^{1/2}X, X\in \cal{L}(H)$ has no solution,
where $\mathcal{L}(H)$ denotes the set of all adjointable operators on $H$.
