AP EAMCET · Maths · Functions
If \(\frac{3 x+2}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}\), then \(A+C-B\) is equal to :
- A 0
- B 2
- C 3
- D 5
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
\(\because \quad \frac{3 x+2}{(x+1)\left(2 x^2+3\right)}=\frac{A}{x+1}+\frac{B x+C}{2 x^2+3}\) \(\Rightarrow \quad 3 x+2=A\left(2 x^2+3\right)+(B x+C)(x+1)\) On putting \(x+1=0\) \(3(-1)+2=A\left[2(-1)^2+3\right]\) \(\Rightarrow \quad-3+2=A(5)\)…
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
- \(R\) divides the line joining two points \(P\) and \(Q\) whose position vectors are \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(-\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) respectively in the ratio \(2: 1\) externally. \(S\) divides \(P Q\) internally in the ratio \(2: 1\). Then, the position vector of the midpoint of the line joining \(R\) and \(S\) isAP EAMCET 2021 Easy
- \(\int_0^3\left|x^2-3 x+2\right| d x=\)AP EAMCET 2018 Medium
- \[
\int \frac{d x}{\sin x+\sin 2 x}=
\]AP EAMCET 2018 Hard - The centroid of the triangle formed by the pair of straight lines \(12 x^2-20 x y+7 y^2=0\) and the line \(2 x-3 y+4=0\) is :AP EAMCET 2006 Easy
- If \(3+i\) and \(2-\sqrt{3}\) are the roots of the equation \(\mathrm{f}(\mathrm{x})=\mathrm{a}_0+\mathrm{a}_1 \mathrm{x}+\mathrm{a}_2 \mathrm{x}^2+\ldots .+\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} ; \mathrm{a}_0, \mathrm{a}_1 \ldots . . \mathrm{a}_{\mathrm{n}} \in \mathbb{Z}\), then the least value of \(\mathrm{n}\) and value of \(\mathrm{a}_0\) are respectively.AP EAMCET 2023 Hard
- The eccentricity of the ellipse of minor-axis \(2 b\), if the line segment joining the foci subtend an angle \(2 \alpha\) at the upper vertex is equal toAP EAMCET 2020 Medium
More PYQs from AP EAMCET
- If \(\sin \left(5 x+\frac{\pi}{4}\right)=0\), then \(x\) is equal toAP EAMCET 2021 Easy
- \(\begin{aligned} & \text { If } y=\tan ^{-1}\left\{\frac{x}{1+\sqrt{1-x^2}}\right\} \\ & +\sin \left\{2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right\} \text {, then } \frac{d y}{d x}=\end{aligned}\)AP EAMCET 2017 Hard
- At a certain place, the angle of dip is \(60^{\circ}\) and the horizontal component of the earth's magnetic field \(\left(B_H\right)\) is \(0.8 \times 10^{-4} \mathrm{~T}\). The earth's overall magnetic field isAP EAMCET 2014 Medium
- The point which lies on the tangent drawn to the curve \(x^4 e^y+2 \sqrt{y+1}=3\) at the point \((1,0)\) isAP EAMCET 2024 Medium
- \(\lim _{x \rightarrow 0} \frac{a^x-1}{\sin (x)}=\)AP EAMCET 2020 Easy
- \(\int_{-1}^{3 / 2}|x \sin \pi x| d x=\)AP EAMCET 2017 Medium