Given the function f(x)=1x3\displaystyle {f{{\left({x}\right)}}}={\frac{{{1}}}{{{x}-{3}}}} and the function g(x)=2x+3\displaystyle {g{{\left({x}\right)}}}={\frac{{{2}}}{{{x}}}}+{3} determine g(f(x))\displaystyle {g{{\left({f{{\left({x}\right)}}}\right)}}}. Simplify your answer.