Question 971206
{{{(x^2+2x+1)/(x-2)=16+(x-3)/(x-2)}}}, a way of saying the same as the description.  The rational expression for the left member must be 16 with a remainder  x-3, and of course the denominator is x-2 for that remainder.  Performing the division should not be necessary.


Multiply both members by  x-2:


{{{x^2+2x+1=16(x-2)+x-3}}}


{{{x^2+2x+1=16x-32+x-3}}}


{{{x^2+2x+1=17x-35}}}


{{{x^2+1=15x-35}}}


{{{x^2-15x+36=0}}}, which seems factorable...


{{{(x-12)(x-3)=0}}}
x=3  or  x=12