Question 731918
2x^3/(2x) = x^2.
x^2*(2x+3)=2x^3+3x^2.
Subtraction gives -2x^2; bring down -x.
Look at -2x^2-x.


-2x^2/(2x)=-x
-x*(2x+3)=-2x^2-3x.
Subtraction gives 2x; bring down the 1.


(2)/().... This 2x+1 looks like a remainder.


Quotient without remainder is {{{x^2-x}}}, and remainder is {{{(2x+1)/(2x+3)}}}.
Continued for one more step, quotient is x^2-x+1, remainder -2.  This should mean, {{{x^2-x+1-2/(2x+3)}}}.