TS EAMCET · Maths · Functions
If \(\frac{x^2+5}{\left(x^2+1\right)(x-2)}=\frac{A}{x-2}+\frac{B x+C}{x^2+1}\), then \(A+B+C=\)
- A -1
- B \(\frac{2}{5}\)
- C -3
- D 0
Answer & Solution
Correct Answer
(C) -3
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & \frac{x^2+5}{\left(x^2+1\right)(x-2)}=\frac{A}{x-2}+\frac{B x+C}{x^2+1} \\ \Rightarrow & x^2+5=A\left(x^2+1\right)+(B x+C)(x-2) \\ \Rightarrow & x^2+5=A x^2+A+B x^2-2 B x+C x-2 C \end{aligned} \] Equating the coefficient of \(x^2, x\) and constant…
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