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TS EAMCET · Maths · Basic of Mathematics

If \(\frac{x-2}{x^2(2 x-3)}=\frac{\mathrm{A}}{x}+\frac{\mathrm{B}}{x^2}+\frac{\mathrm{C}}{2 x-3}\) then \(2(\mathrm{~A}-\mathrm{C})=\)

  1. A \(3 \mathrm{~B}\)
  2. B \(2 \mathrm{~B}\)
  3. C 0
  4. D \(\mathrm{B}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\mathrm{B}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \frac{\mathrm{x}-2}{\mathrm{x}^2(2 \mathrm{x}-3)}=\frac{\mathrm{A}}{\mathrm{x}}+\frac{\mathrm{B}}{\mathrm{x}^2}+\frac{\mathrm{C}}{2 \mathrm{x}-3} \\ & \Rightarrow(\mathrm{x}-2)=\mathrm{Ax}(2 \mathrm{x}-3)+\mathrm{B}(2 \mathrm{x}-3)+C \cdot \mathrm{x}^2…