The fraction frac{x^2}{(x-a)(x-b)} is | vedclass

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Question

(B) Consider the expression $\frac{x^2}{(x-a)(x-b)}$.Expanding the denominator,we get $\frac{x^2}{x^2 - (a+b)x + ab}$.The degree of the numerator is $

Vedclass · Accepted Answer

always an improper partial fraction

Vedclass · Answer

(B) Consider the expression $\frac{x^2}{(x-a)(x-b)}$.Expanding the denominator,we get $\frac{x^2}{x^2 - (a+b)x + ab}$.The degree of the numerator is $2$ and the degree of the denominator is $2$.$A$ rational function $\frac{P(x)}{Q(x)}$ is called an improper fraction if the degree of $P(x)$ is greater than or equal to the degree of $Q(x)$.Since the degrees are equal,the given fraction is always an improper partial fraction.Therefore,option $B$ is correct.

The fraction $\frac{x^2}{(x-a)(x-b)}$ is

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