If x2-x-1-x2-2x-1-A-B-x-1-C-x-12- then A-B-

Explanation for the correct option:x^2+x+1/x^2+2x+1=A+B/x+1+C/(x+1)^2Taking RHSA+B/x+1+C/(x+1)^20ex0ex=A(x+1)^2+B(x+1)+C/(x+1)^20ex0ex=Ax^2+2Ax+A+Bx+B+C/x^2+2x+ ...

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Byju's Answer

Standard XIII

Physics

Basic Differentiation Rule

If x2+x+1/x2+...

Question

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

$4$

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$4 C + 1$

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$3 C$

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$2$

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Solution

The correct option is D
$2$

Explanation for the correct option:
$\frac{x^{2} + x + 1}{x^{2} + 2 x + 1} = A + \frac{B}{x + 1} + \frac{C}{{(x + 1)}^{2}}$
Taking RHS
$A + \frac{B}{x + 1} + \frac{C}{{(x + 1)}^{2}} = \frac{A {(x + 1)}^{2} + B (x + 1) + C}{{(x + 1)}^{2}} = \frac{A x^{2} + 2 A x + A + B x + B + C}{x^{2} + 2 x + 1} = \frac{A x^{2} + (2 A + B) x + A + B + C}{x^{2} + 2 x + 1}$
So,
$\begin{array}{rcl} \frac{x^{2} + x + 1}{x^{2} + 2 x + 1} & = & \frac{A x^{2} + (2 A + B) x + A + B + C}{x^{2} + 2 x + 1} \\ \Rightarrow & x^{2} + x + 1 = A x^{2} + (2 A + B) x + A + B + C \end{array}$
On comparing the coefficients, we get
$A = 1$ and
$\begin{array}{rcl} 2 A + B & = & 1 \\ \Rightarrow B & = & - 1 \end{array}$
Therefore, $A - B = 1 + 1 = 2$
Hence. option D is correct.

Suggest Corrections

If x2+x+1x2+2x+1=A+Bx+1+Cx+12, then A-B=

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