Does it follow that r(x)+p(x) is a rational function (and not a polynomial)? Suppose r(x)≠0 is a rational function (and not a polynomial) p(x) is a polynomial function of x∈R.

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Does it follow that r(x)+p(x) is a rational function (and not a polynomial)?  Suppose r(x)≠0 is a rational function (and not a polynomial)  p(x) is a polynomial function of x∈R.

Alexandra Haynes · Accepted Answer

Yes. Suppose that r(x)+p(x)=s(x) were a polynomial. Then also r(x)=s(x)=p(x) would be a polynomial, hence r(x) is a polynomial, contradiction.

Does it follow that r(x)+p(x) is a rational function (and not a polynomial)? Suppose r(x)≠0...

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