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
- A \(4 C\)
- B \(4 C+1\)
- C \(3 C\)
- D \(2 \mathrm{C}\)
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…
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