Can any quotient of polynomials be decomposed into at least two partial fractions? If so, explain why, and if not, give an example of such a fraction

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Keith Dooley · Accepted Answer

Given information:  The given statement is,  Any quotient of polynomials can be decomposed into at least two partial fractions.  For decompositions of partial fractions, the polynomial expression should be proper, that is, the degree of numerator should be less than that of the denominator.  Hence, no quotient of polynomials can be decomposed into at least two partial fractions as the decomposition is done on the denominator part and not on the quotient part.  Consider the polynomial expression,  x2+1x2−1  Since, the degree of the numerator and the denominator is equal, thus the expression is changed by long division method as,  1+2x2−1  Thus, the quotient part is left alone and then the partial fraction is preformed on 2x2−1

Can any quotient of polynomials be decomposed into at least two partia

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