Simplify the expression
$\displaystyle {\frac{{{\frac{{{4}}}{{{x}-{1}}}}-{\frac{{{1}}}{{{x}+{1}}}}}}{{{\frac{{{x}}}{{{x}-{1}}}}+{\frac{{{1}}}{{{x}+{1}}}}}}}$
and give your answer in the form of
$\displaystyle {\frac{{{f{{\left({x}\right)}}}}}{{{g{{\left({x}\right)}}}}}}.$

Your answer for the function $\displaystyle {f{{\left({x}\right)}}}$ is : Preview Question 6 Part 1 of 2  
Your answer for the function $\displaystyle {g{{\left({x}\right)}}}$ is : Preview Question 6 Part 2 of 2