Question

Resolve in to partial fraction :
x^2 - x+3/(X - 2) (x^2+1)​

Answer 1

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Resolve

(x+2)(x

2

+1)

x

2

−3

into partial fractions

Hard

Solution

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(x+2)(x

2

+1)

x

2

−3

=

x+2

A

+

x

2

+1

Bx+C

∴x

2

−3=A(x

2

+1)+(Bx+C)(x+2)

⇒x

2

−3=Ax

2

+A+Bx

2

+2Bx+Cx+2C

Comparing the coefficients of x

2

,x and constant terms, we have

1=A+B ..(1)

0=2B+C ...(2)

−3=A+2C ...(3)

Subtracting equation (1) from (3), we have

2C−B=−3−1=−4 ...(4)

Multiplying equation (4) by 2 and adding that to equation (2), we have

4C−2B+2B+C=−8

∴C=−

5

8

∴A=−3−2C=

5

1

,B=1−A=

5

4

∴

(x+2)(x

2

+1)

x

2

−3

=

5(x+2)

1

+

5(x

2

+1)

4x−8