AP EAMCET · Maths · Basic of Mathematics
If the equivalent partial fraction of \(\frac{x^3}{(2 x-1)(x+2)(x-3)}\)
is of the form \(A+\frac{B}{2 x-1}+\frac{C}{x+2}+\frac{D}{x-3}\) then the value of \(A+B+C=\)
- A \(-8 / 25\)
- B \(4 / 25\)
- C \(-1 / 50\)
- D \(1 / 2\)
Answer & Solution
Correct Answer
(B) \(4 / 25\)
Step-by-step Solution
Detailed explanation
\(\frac{x^3}{(2 x-1)(x+2)(x-3)}\) \(=A+\frac{B}{(2 x-1)}+\frac{C}{(x+2)}+\frac{D}{(x-3)}\) \(\begin{aligned} & x^3=A(2 x-1)(x+2)(x-3)+\mathrm{B}(x+2)(x-3)+\mathrm{C} \\ & (2 x-1)(x-3)+\mathrm{D}(2 x-1)(x+2) \ldots(\mathrm{i})\end{aligned}\) Put \(x=1 / 2\)…
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