Final answer:
The question is regarding the partial fraction decomposition of the expression x´ - 2x³ + x²/x² - 2x + 1. The correct approach involves factoring the denominator to (x-1)² and expressing the original fraction as a sum of simpler fractions. The options provided do not match this method.
Step-by-step explanation:
The student's question is asking for the partial fraction decomposition of the given rational expression x⁴−2x³+x²/x²−2x+1. To decompose a fraction, you first have to factor the denominator and then express the original fraction as a sum of fractions with the factored denominators. In this case, the denominator x²-2x+1 factors to (x-1)², which means we're looking for constants A and B such that our expression equals A/(x-1) + B/(x-1)².
However, none of the options provided perfectly match the partial fraction decomposition steps or the factored denominator, indicating a possible misunderstanding of how to approach the decomposition. Since the student's statement contains unrelated equations interspersed with the question, the response focuses on clarifying the correct method to perform partial fraction decomposition.