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AP EAMCET · Maths · Quadratic Equation

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

  1. A \(4 C\)
  2. B \(4 C+1\)
  3. C \(3 C\)
  4. D \(2 \mathrm{C}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \mathrm{C}\)

Step-by-step Solution

Detailed explanation

It is given that, \(\begin{aligned} & \frac{x^2+x+1}{x^2+2 x+1}=A+\frac{B}{x+1}+\frac{C}{(x+1)^2} \\ \Rightarrow \quad & x^2+x+1=A\left(x^2+2 x+1\right)+B(x+1)+C \\ \Rightarrow \quad & x^2+x+1=A x^2+(2 A+B) x+(A+B+C) \end{aligned}\) On comparing the coefficient of different…