AP EAMCET · Maths · Quadratic Equation
If \(\frac{x+2}{x^2-3}\) is one of the partial fractions of \(\frac{3 x^3-x^2-2 x+17}{x^4+x^2-12}\), then the other partial fraction of it is
- A \(\frac{2 x+3}{x^2-4}\)
- B \(\frac{3 x+2}{x^2+4}\)
- C \(\frac{2 x-3}{x^2+4}\)
- D \(\frac{3 x-2}{x^2-4}\)
Answer & Solution
Correct Answer
(C) \(\frac{2 x-3}{x^2+4}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {Since } \frac{3 x^3-x^2-2 x+17}{x^4+x^2-12} \\ & =\frac{3 x^3-x^2-2 x+17}{\left(x^2-3\right)\left(x^2+4\right)}=\frac{x+2}{x^2-3}+\frac{A x+B}{x^2+4} \\ & \Rightarrow \frac{A x+B}{x^2+4}=\frac{3 x^3-x^2-2…
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