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AP EAMCET · Maths · Basic of Mathematics

If \(\frac{2 x^4-3 x^2+4}{\left(x^2+1\right)\left(x^2+2\right)}=a+\frac{p x+q}{x^2+1}+\frac{m x+n}{x^2+2}\), then \(\frac{n}{q}=\)

  1. A \(p+m-a\)
  2. B \(\frac{p+m}{a}\)
  3. C \(\frac{a}{p+m}\)
  4. D \(p+m+a\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(p+m-a\)

Step-by-step Solution

Detailed explanation

\(a = 2\) \(\frac{2x^4-3x^2+4}{(x^2+1)(x^2+2)} - 2 = \frac{2x^4-3x^2+4 - 2(x^4+3x^2+2)}{(x^2+1)(x^2+2)} = \frac{-9x^2}{(x^2+1)(x^2+2)}\) Compare \(\frac{-9x^2}{(x^2+1)(x^2+2)} = \frac{px+q}{x^2+1} + \frac{mx+n}{x^2+2}\) \(p=0\), \(m=0\) For \(x^2=-1\):…