Best weighted approximation of some kernels on the real axis

We calculate the exact value and find the polynomial of the best weighted polynomial approximation of kernels of the form $\frac{A+Bt}{(t^2+{\lambda }^2{)}^{s+1}}$, where $A$ and $B$ are fixed complex numbers, $\lambda >0$, $s\in \mathbb{N}$, in the mean square metric.