AP EAMCET · Maths · Quadratic Equation
If \(\frac{x}{(x-1)\left(x^2+1\right)^2}=\frac{1}{4}\left[\frac{1}{x-1}-\frac{x+1}{x^2+1}\right]+y\), then \(\mathrm{y}=\)
- A \(\frac{1}{2}\left[\frac{1-x}{\left(x^2+1\right)^2}\right]\)
- B \(\frac{1+x}{3\left(x^2+1\right)^2}\)
- C \(\frac{1-x}{\left(x^2-1\right)^2}\)
- D \(\frac{1+x}{\left(x^2+1\right)^2}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\left[\frac{1-x}{\left(x^2+1\right)^2}\right]\)
Step-by-step Solution
Detailed explanation
Let \(f(x)= \begin{cases}\frac{1}{2}(-x-) & \text { if } x 1\end{cases}\) \(\Rightarrow \mathrm{x}=\mathrm{A}\left(\mathrm{x}^2+1\right)^2+(\mathrm{Bx}+\mathrm{c})(\mathrm{x}-1)\left(\mathrm{x}^2+1\right)+(\mathrm{Dx}+\mathrm{E})(\mathrm{x}-1)\) On putting…
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