Consider the rational function 2x^ 3 +3x^ 2 +1 x^ 2 -1

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the rational function 2x3+3x2+1x2−1.\frac{2x^{3}+3x^{2}+1}{x^{2}-1}. (i) Express it as the sum of a polynomial and a proper fraction. (ii) Write the general partial-fraction decomposition of the proper fraction obtained in part (i) (do not evaluate the constants).

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