Simplify the expression
x24x+4x23x+2\displaystyle {\frac{{{x}^{{2}}-{4}{x}+{4}}}{{{x}^{{2}}-{3}{x}+{2}}}}
and give your answer in the form of
f(x)g(x).\displaystyle {\frac{{{f{{\left({x}\right)}}}}}{{{g{{\left({x}\right)}}}}}}.

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 :