I know that for polynomials P , Q , the equation P ( z ) &#x2261;<!-- ≡ -

meindwrhc

meindwrhc

Answered question

2022-05-28

I know that for polynomials P , Q, the equation P ( z ) Q ( z ) implies that they are of the same degree and have the same coefficients. Is there an analogous result for rational fucntions? That is, if R , S are two rational functions and R ( z ) = S ( z ) for all z what is the relationship between R and S?

Answer & Explanation

minnegodks

minnegodks

Beginner2022-05-29Added 10 answers

If R ( z ) = S ( z ) for all z such that this equation makes sense, then R ( z ) S ( z ) = 0 for all z. Now, R S is a rational function that's equal to zero everywhere where it is defined. You can easily show that such function is given by 0 / Q ( z ) where Q is some polynomial.

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