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AP EAMCET · Maths · Basic of Mathematics

If \(\frac{6 x^3+7 x^2-14 x+11}{6 x^3+x^2-10 x+3}=a+\frac{b}{x+p}+\frac{c}{q x+3}+\frac{d}{3 x+p}\) then \(\frac{a+b}{p+q}=\)

  1. A 2
  2. B 3
  3. C \(-\frac{2}{5}\)
  4. D \(\frac{2}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) 2

Step-by-step Solution

Detailed explanation

Given that: \(\frac{6 x^3+7 x^2-14 x+11}{6 x^3+x^2-10 x+3}=a+\frac{b}{x+p}+\frac{c}{q x+3}+\frac{d}{3 x+p}\) ...(i) \(=\frac{6 x^3+7 x^2-14 x+11}{6 x^3+x^2-10 x+3}=1+\frac{6 x^2-4 x+8}{6 x^3+x^2-10 x+3}\) \(=1+\frac{6 x^2-4 x+8}{(x-1)(3 x-1)(2 x+3)}\) ...(ii) Now let…