Mathematics

If $$\displaystyle \frac{(x-1)^2}{x^3+x}=\frac{A}{x}+\frac{Bx+C}{x^2+1}$$, then $$A=..., B=..., C=...$$


ANSWER

$$A=1,B=0,C=-2$$


SOLUTION
$$\displaystyle \frac { (x-1)^{ 2 } }{ x^{ 3 }+x } =\frac { A }{ x } +\frac { Bx+C }{ x^{ 2 }+1 } $$

$$\Rightarrow { \left( x-1 \right)  }^{ 2 }=A\left( { x }^{ 2 }+1 \right) +\left( Bx+C \right) x$$

$$ \Rightarrow \left( { x }^{ 2 }-2x+1 \right) =A\left( { x }^{ 2 }+1 \right) +B{ x }^{ 2 }+Cx$$

$$ \Rightarrow \left( { x }^{ 2 }-2x+1 \right) =(A+B){ x }^{ 2 }+Cx+A$$

On comparing coefficients 

$$A+B=1,C=-2,A=1\Rightarrow A=1,B=0,C=-2$$

Hence, option 'A' is correct.
View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Hard
Solve $$\displaystyle\int\dfrac{e^{x}(1+x)}{\cos^{2}(e^{x}x)}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 One Word Medium
$$\displaystyle \int_{0}^{\pi }x\log \sin x= \frac{\pi ^{k}}{m}\log \frac{1}{n}.$$.Find $$k+m+n$$ ?

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Integrate with respect to $$x$$:
$$2x^{3}\ e^{x^{2}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
Evaluate the following integral:
$$\displaystyle\int^a_0\sqrt{a^2-x^2}dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
The value of $$\displaystyle\int\limits_{0}^{\dfrac{\pi}{2}}\dfrac{2^{\sin x}}{2^{\sin x}+2^{\cos x}}dx$$ is
  • A. $$\pi$$
  • B. $$0$$
  • C. none of these
  • D. $$\dfrac{\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer