AP EAMCET · Maths · Quadratic Equation
If \(\frac{1-x+6 x^2}{1-x^3}=\frac{A}{x}+\frac{B}{1+x}+\frac{C}{1+x}\), then \(A\) is equal to
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(1\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} \frac{1-x+6 x^2}{x-x^3} & =\frac{A}{x}+\frac{B}{1-x}+\frac{C}{1+x} \\ \Rightarrow \quad 1-x+6 x^2 & =A\left(1-x^2\right)+B x(1+x)+C x(1-x) \end{aligned} \] Put \(x=0\), then \(A=1\)
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