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(J[itex]^{T}[/itex]R[itex]^{-1}[/itex]J + P[itex]^{-1}[/itex])[itex]^{-1}[/itex]J[itex]^{T}[/itex]R[itex]^{-1}[/itex]

=

PJ[itex]^{T}[/itex](JPJ[itex]^{T}[/itex] + R)[itex]^{-1}[/itex]

J is arbitrary size, P and R are square though not necessarily equal. Can anyone help? I thought binomial inverse theorem would save me but I haven't been able to get rid of the extraneous terms.