AP EAMCET · Maths · Basic of Mathematics
If the equivalent partial fraction of \(\frac{x^3}{(2 x-1)(x+2)(x-3)}\) is given by. \(A+\frac{B}{2 x-1}+\frac{C}{x+2}+\frac{D}{x-3}\), then the value of \(C\) is
- A \(\frac{1}{2}\)
- B \(-\frac{1}{50}\)
- C \(-\frac{8}{25}\)
- D \(\frac{27}{25}\)
Answer & Solution
Correct Answer
(C) \(-\frac{8}{25}\)
Step-by-step Solution
Detailed explanation
Here, \(\begin{array}{l} \frac{x^3}{(2 x-1)(x+2)(x-3)}=A+\frac{B}{2 x-1}+\frac{C}{x+2}+\frac{D}{x-3} \\ \Rightarrow x^3=A(2 x-1)(x+2)(x-3)+B(x+2)(x-3) . \\ \quad+C(2 x-1)(x-3)+D(2 x-1)(x+2) \end{array}\)…
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