$${\frac{\left[{\left(\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right){\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}\right]}{\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{x}}\right)}}$$
There is nothing to simplify here.
$$\frac{(1+2x)\sqrt{1+x}}{1-x}$$
.$${\frac{\left[{\left(\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right){\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)}\right]}{\left({\mathtt{1}}{\mathtt{\,-\,}}{\mathtt{x}}\right)}}$$
There is nothing to simplify here.
$$\frac{(1+2x)\sqrt{1+x}}{1-x}$$