AP EAMCET · Maths · Basic of Mathematics
\(\frac{x^4}{\left(x^2+1\right)\left(x^2+3\right)}=\)
- A \(\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+3}\) for some \(A, B, C, D \in R \backslash\{0\}\)
- B \(\frac{A x+B}{x^2+1}+\frac{C x}{x^2+1}\) for some \(A, B, C \in R \backslash\{0\}\)
- C \(\frac{A x}{x^2+1}+\frac{B x}{x^2+3}\) for some \(A, B \in R \backslash\{0\}\)
- D \(1+\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+3}\) for some \(A, B, C, D \in R\)
Answer & Solution
Correct Answer
(D) \(1+\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+3}\) for some \(A, B, C, D \in R\)
Step-by-step Solution
Detailed explanation
\begin{aligned} \frac{x^4}{\left(x^2+1\right)\left(x^2+3\right)} & =\frac{\left(x^2+1\right)\left(x^2+3\right)-3 x^2-x^2-3}{\left(x^2+1\right)\left(x^2+3\right)} \\ & =1-\frac{4 x^2+3}{\left(x^2+1\right)\left(x^2+3\right)} \\ & =1+\frac{A x+B}{x^2+1}+\frac{C…
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
- Length of the common chord of two circles of same radius is \(2 \sqrt{17}\). If one of the two circles is \(x^2+y^2+6 x+4 y-12=0\), then acute angle between the two circles isAP EAMCET 2025 Medium
- If \(f(x)=\frac{1}{\sqrt{x+2 \sqrt{2 x-4}}}+\frac{1}{\sqrt{x-2 \sqrt{2 x-4}}}\) for \(x>2\), then \(f(11)\) is equal toAP EAMCET 2003 Hard
- If \(I_n=\int \frac{t^{2 n}}{1+t^2} d t\), then \(I_{n+1}=\)AP EAMCET 2017 Medium
- In a triangle, if \(b=20, c=21\) and \(\sin A=\frac{3}{5}\), then \(a\) is equal to :AP EAMCET 2003 Easy
- If \(b>a\), then \(\int_a^b \frac{d x}{\sqrt{(x-a)(b-x)}}\) is equal toAP EAMCET 2021 Hard
- If \(A(2,4,-1), B(3,6,-1)\) and \(C(4,5,1)\) are three consecutive vertices of a parallelogram, then its fourth vertex isAP EAMCET 2019 Easy
More PYQs from AP EAMCET
- Match the following:
The correct answer isList - I (colloidal solution) List - II (Use) Colloidal antimony I) Eye lotion Argyrol II) Intramuscular injection Colloidal gold III) Kalaazar Milk of magnesia IV) Stomach disorders AP EAMCET 2025 Easy - Three thin uniform rods each of mass M and length L are placed along the three axes of a cartesian coordinate system with one end of all the rods at origin. The moment of inertia of the system of the rods about z -axis isAP EAMCET 2025 Medium
- The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is :AP EAMCET 2006 Medium
- Let \(A B C D E F\) be a regular hexagon with the vertices \(A, B, C, D, E, F\) counterclock-wise. Then the vector \(\mathbf{A B}+\mathbf{A F}+\mathbf{C D}+\mathbf{E F}\) is equal toAP EAMCET 2020 Medium
- Among the 4 digit numbers formed using the digits \(0,1,2,3,4\) when repetition of digits allowed, the number of numbers which are divisible by 4 isAP EAMCET 2024 Easy
- The angle between lines represented by \(\left(\sin ^2 \alpha\right) y^2-2 x y\left(\cos ^2 \alpha\right)+\left(\cos ^2 \alpha-1\right) x^2=0\) isAP EAMCET 2021 Easy