The divisor divides evenly into the numerator. The answer is:
or after multiplying both sides by (x-1):
Divide the leading term 
of the numerator polynomial by the leading term x of the divisor:
Multiply "back": 
, and subtract:
Divide the leading term 
of the bottom polynomial by the leading term x of the divisor:
Multiply back: 
, and subtract:
One more step! Divide again:
Multiply "back", and subtract:
The divisor divides evenly into the numerator. The answer is:
or after multiplying both sides by (x-1):
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Helmut Knaust