Let $f(x)=x^{2}+3$ , And $g(x)=\frac{1}{x}+1$ Does $g(f(x))=\frac{1 x^{2}+1}{x^{2}+3} ?$

Let $f(x)=x^{2}+3$ , and $g(x)=\frac{1}{x}+1$ . Does $g(f(x))=\frac{1 x^{2}+1}{x^{2}+3} ?$