The fundamental theorem of algebraic $K$-theory says that $K_1(R[t,t^{-1}])\cong K_1(R)\oplus K_0(R)\oplus NK_1(R)\oplus NK_1(R)$
On the page 153 of Rosenberg's book on algebraic $K$-theory, he said it follows immediately that $K_0(R)=\text{coker}\{K_1(R[t])\oplus K_1(R[t^{-1}])\longrightarrow K_1(R[t,t^{-1}])\}$.
But this result is not so obvious to me, and I even don't know what the map $K_1(R[t])\oplus K_1(R[t^{-1}])\longrightarrow K_1(R[t,t^{-1}])$ is.
How to prove it?