Simplify the expression and give your answer in the form of f(x)g(x).\displaystyle {\frac{{{f{{\left({x}\right)}}}}}{{{g{{\left({x}\right)}}}}}}.

1x2+4x+41x22x8\displaystyle {\frac{{{1}}}{{{x}^{{2}}+{4}{x}+{4}}}}-{\frac{{{1}}}{{{x}^{{2}}-{2}{x}-{8}}}}


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