If frac{(x - 1)^2}{x^3 + x} = frac{A}{x} + fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the partial fraction decomposition: $\frac{(x - 1)^2}{x(x^2 + 1)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$.Expanding the numerator on the lef

Vedclass · Accepted Answer

$A = 1, B = 0, C = -2$

Vedclass · Answer

(A) Given the partial fraction decomposition: $\frac{(x - 1)^2}{x(x^2 + 1)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$.Expanding the numerator on the left side: $\frac{x^2 - 2x + 1}{x(x^2 + 1)} = \frac{A(x^2 + 1) + x(Bx + C)}{x(x^2 + 1)}$.Equating the numerators: $x^2 - 2x + 1 = A(x^2 + 1) + Bx^2 + Cx$.$x^2 - 2x + 1 = (A + B)x^2 + Cx + A$.Comparing the coefficients of $x^2$,$x$,and the constant term:$1$) $A + B = 1$$2$) $C = -2$$3$) $A = 1$Substituting $A = 1$ into equation $(1)$: $1 + B = 1 \implies B = 0$.Thus,$A = 1, B = 0, C = -2$.

If $\frac{(x - 1)^2}{x^3 + x} = \frac{A}{x} + \frac{Bx + C}{x^2 + 1}$,then

Similar Questions

The wavelengths of two sound notes in air are $\frac{40}{195} ~m$ and $\frac{40}{193} ~m$. Each note produces $9$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is

The displacement of a particle varies according to the relation $x = 3 \sin(100t) + 8 \cos^2(50t)$. Which of the following is $INCORRECT$ about this motion?

Which one of the following halogens liberates oxygen,when passed through hot concentrated $KOH$ solution?

Which of the following compounds exhibits optical isomerism?

The osmotic pressure of a $5\% \, w/v$ solution of cane sugar at $150 \, ^\circ C$ is ......... $atm$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module