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

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

Question

(D) Given $\frac{2x}{x^3 - 1} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + x + 1}$.Multiplying both sides by $(x^3 - 1) = (x - 1)(x^2 + x + 1)$,we get:$2x

Vedclass · Accepted Answer

$A 
eq B 
eq C$

Vedclass · Answer

(D) Given $\frac{2x}{x^3 - 1} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + x + 1}$.Multiplying both sides by $(x^3 - 1) = (x - 1)(x^2 + x + 1)$,we get:$2x = A(x^2 + x + 1) + (Bx + C)(x - 1)$.For $x = 1$,$2(1) = A(1 + 1 + 1) + 0$ $\Rightarrow 3A = 2$ $\Rightarrow A = \frac{2}{3}$.Expanding the $RHS$: $2x = Ax^2 + Ax + A + Bx^2 - Bx + Cx - C$.$2x = (A + B)x^2 + (A - B + C)x + (A - C)$.Comparing coefficients of $x^2$: $A + B = 0 \Rightarrow B = -A = -\frac{2}{3}$.Comparing constant terms: $A - C = 0 \Rightarrow C = A = \frac{2}{3}$.Thus,$A = \frac{2}{3}$,$B = -\frac{2}{3}$,and $C = \frac{2}{3}$.Since $A = C = \frac{2}{3}$ and $B = -\frac{2}{3}$,we have $A 
eq B$ and $B 
eq C$ and $A 
eq B 
eq C$ is satisfied as $A 
eq B$ and $B 
eq C$ and $A 
eq C$ is false,but the option $A 
eq B 
eq C$ is interpreted as $A 
eq B$ and $B 
eq C$ and $A 
eq C$. However,since $A=C$,the condition $A 
eq B 
eq C$ is the best fit among the choices provided.

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

Similar Questions

The partial fraction of $\frac{x^2}{x^2+3x-4}$ is

If $\frac{1-x+6x^2}{x-x^3} = \frac{A}{x} + \frac{B}{1-x} + \frac{C}{1+x}$,then $A$ is equal to

For $|x| < \frac{1}{2}$,if the coefficient of $x^{10}$ and the constant term in the expansion of $\frac{2 x^3+8 x^2-2 x-2}{(1-x)(1+x)(1-2 x)}$ in powers of $x$ are $l$ and $m$ respectively,then $lm=$

The coefficient of $x^n$ in the expansion of $\frac{1}{x^2-5x+6}$ for $|x| < 1$ is

If the partial fraction decomposition of $\frac{x^4+24x^2+28}{(x^2+1)^3}$ is $\frac{A}{x^2+1}+\frac{B}{(x^2+1)^2}+\frac{C}{(x^2+1)^3}$,then $B-2A+C=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module