Let $G$ be a linear algebraic group over $\mathbb C$ (say $SL_r$) consider a formal power series $$g(t)\in G(\mathbb C((t)))$$ My question is: Is it possible to decompose $g$ as $$g=ha$$ with $h\in G(\mathbb C[1/t]) $ and $a\in G(\mathbb C[[t]])$

N.B: the important case that I need is $SL_r$ and $GL_r$.

Thanks