Divide the leading term 
of the numerator polynomial by the leading term 2x of the divisor:
Multiply "back": 
, and subtract:
Divide the leading term 
of the bottom polynomial by the leading term 2x of the divisor:
Multiply back:
and subtract:
One more step! Divide again:
Multiply "back", and subtract:
Consequently, we obtain:
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Helmut Knaust