Question 1031494
Work it backwards to see if you get the original numerator. 
As a simpler example,
{{{(2x^2+2x+9)/(x+3)=(2x-4)+21/(x+3)}}}
So then multiplying both sides by {{{x+3}}},
{{{2x^2+2x+9=(2x-4)(x+3)+21}}}
{{{2x^2+2x+9=2x^2+6x-4x-12+21}}}
{{{2x^2+2x+9=2x^2+2x+9}}}
So then verify that,
{{{5x^4-4x^3+3x^2-2x+1=(5x^3+6x^2+15x+28)(x-2)+57}}}