CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

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


A
4C
loader
B
4C+1
loader
C
3C
loader
D
2C
loader

Solution

The correct option is C $$2C$$
Given, $$\dfrac{x^{2}+x+1}{(x+1)^{2}}=A+\dfrac{B}{(x+1)}+\dfrac{C}{(x+1)^{2}}$$
$$\dfrac{x^{2}+x+1}{(x+1)^{2}}=\dfrac{A(x+1)^{2}+B(x+1)+C}{(x+1)^{2}}$$
$$x^{2}+x+1=A(x+1)^{2}+B(x+1)+C$$
Let us put $$x=-2$$
$$3-c=A-B$$
$$A-B=2$$
and
$$f(-1)=c=1$$
So $$A-B=2C$$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image