AP EAMCET · Maths · Basic of Mathematics
If \(\frac{3 x+1}{(x-1)\left(x^2+2\right)}=\frac{A}{x-1}+\frac{B x+C}{x^2+2}\), then \(5(A-B)=\)
- A \(\mathrm{A}+\mathrm{C}\)
- B \(8 C\)
- C \(\mathrm{C}+8\)
- D \(\frac{C}{8}\)
Answer & Solution
Correct Answer
(B) \(8 C\)
Step-by-step Solution
Detailed explanation
\(3x+1 = A(x^2+2) + (Bx+C)(x-1)\) Set \(x=1\): \(4 = A(1^2+2) \Rightarrow 4 = 3A \Rightarrow A=\frac{4}{3}\) Coeff of \(x^2\): \(0 = A+B \Rightarrow B = -A = -\frac{4}{3}\) Coeff of constant: \(1 = 2A-C \Rightarrow C = 2A-1 = 2(\frac{4}{3})-1 = \frac{8}{3}-1 = \frac{5}{3}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \[
\left[\sqrt{2}\left(\cos 56^{\circ} 15^{\prime}+i \sin 56^{\circ} 15^{\prime}\right)\right]^8=
\]AP EAMCET 2023 Easy - If \(y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\ldots . \infty}}}\) then the value of \(\frac{d^2 y}{d x^2}\) at the point \((\pi, 1)\) isAP EAMCET 2024 Easy
- \(\lim _{x \rightarrow 0} \frac{1-\cos x \cos 2 x}{\sin ^2 x}=\)AP EAMCET 2024 Medium
- Coefficient of \(x^2\) in the expansion of \(\left(x^2+x-2\right)^5\) isAP EAMCET 2025 Medium
- The range of the real valued function \(f(x)=\sqrt{9-x^2}\) isAP EAMCET 2023 Easy
- If
\[
\int \frac{x-\sin x}{1+\cos x} d x=x \tan \left(\frac{x}{2}\right)+p \log \left|\sec \left(\frac{x}{2}\right)\right|+C,
\]
then \(p\) is equal toAP EAMCET 2013 Medium
More PYQs from AP EAMCET
- A matrix whose elements \(a_{i j}\) are defined by
\(a_{i j}=\frac{1}{3}|i-5 j|, i, j=1,2,3 \text { is }\)AP EAMCET 2023 Easy - If in , then which of the following holds?AP EAMCET 2021 Easy
- Dimensions of \(\varepsilon_0\) areAP EAMCET 2020 Easy
- If \(\int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}=\frac{A \sqrt{x}}{\sqrt{1-x}}+\frac{B}{\sqrt{1-x}}+C\), where \(C\) is real constant, then \(A+B\) equals toAP EAMCET 2014 Hard
- The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one ring isAP EAMCET 2021 Easy
- Which one of the following is an anionic detergent?AP EAMCET 2017 Easy