Which of the following is an improper rationa | vedclass

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Question

(D) rational fraction $\frac{p(x)}{q(x)}$ is called an improper rational fraction if the degree of the numerator $p(x)$ is greater than or equal to th

Vedclass · Accepted Answer

$\frac{x^2+1}{x^2-1}$

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(D) rational fraction $\frac{p(x)}{q(x)}$ is called an improper rational fraction if the degree of the numerator $p(x)$ is greater than or equal to the degree of the denominator $q(x)$.$(a)$ For $\frac{x^2+1}{(x^2+2)(x^2+x+1)}$,degree of $p(x) = 2$ and degree of $q(x) = 4$. Since $2 $(b)$ For $\frac{x^2+1}{(x+3)(x^2-x+1)}$,degree of $p(x) = 2$ and degree of $q(x) = 3$. Since $2 $(c)$ For $\frac{x}{x^2+3x+1}$,degree of $p(x) = 1$ and degree of $q(x) = 2$. Since $1 $(d)$ For $\frac{x^2+1}{x^2-1}$,degree of $p(x) = 2$ and degree of $q(x) = 2$. Since the degree of the numerator is equal to the degree of the denominator,it is an improper rational fraction.

Which of the following is an improper rational fraction?

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