Simplify the expression
1+3c313c3\displaystyle {\frac{{{1}+{\frac{{{3}}}{{{c}-{3}}}}}}{{{1}-{\frac{{{3}}}{{{c}-{3}}}}}}}
and give your answer in the form of
f(c)g(c).\displaystyle {\frac{{{f{{\left({c}\right)}}}}}{{{g{{\left({c}\right)}}}}}}.

Your answer for the function f(c)\displaystyle {f{{\left({c}\right)}}} is :  
Your answer for the function g(c)\displaystyle {g{{\left({c}\right)}}} is :