(B) rational expression $\frac{P(x)}{Q(x)}$ is called an improper fraction if the degree of the numerator $P(x)$ is greater than or equal to the degre

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(B) rational expression $\frac{P(x)}{Q(x)}$ is called an improper fraction if the degree of the numerator $P(x)$ is greater than or equal to the degree of the denominator $Q(x)$.Here,the degree of the numerator $x^4$ is $4$ and the degree of the denominator $x^3-3x+2$ is $3$.Since $4 \geq 3$,the expression is an improper fraction.

Class 11 Mathematics Basic of Logarithms Partial fractions

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$\frac{x^4}{x^3-3x+2}$ is a

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Proper fraction
B
Improper fraction
C
Mixed fraction
D
Not a fraction

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If $\frac{x^2+x+1}{x^2+2x+1}=A+\frac{B}{x+1}+\frac{C}{(x+1)^2}$,then $A-B$ is equal to

EasyAP EAMCET 2020

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$\begin{aligned} & \frac{x^2+x+1}{(x-1)(x-2)(x-3)}=\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3} \\ & \Rightarrow A+C= \end{aligned}$

DifficultAP EAMCET 2011

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If $\frac{x^4}{(x-1)(x-2)(x-3)}=p(x)+\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}$ then $p\left(\frac{3}{2}\right)+C=$

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If $\frac{x-4}{x^2-5x+6}$ can be expanded in the ascending powers of $x$,then the coefficient of $x^3$ is

MediumTS EAMCET 2004

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When $|x| < \frac{1}{2}$,the coefficient of $x^4$ in the expansion of $\frac{3x^2-5x+3}{(x-1)(2x+1)(x+3)}$ is

MediumAP EAMCET 2019

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