Question

resolve 3x^2+x-2/(x-2) ^2(1-2x) into partial fraction​

Answer 1

Answer:

The table give general form of the partial fractions :

So ,

(1−2x)(1−x

2

)

1+3x+2x

2

=

(1−2x)(1−x)(1+x)

1+3x+2x

2

=>

(1−2x)(1−x)(1+x)

1+3x+2x

2

=

1−2x

A

+

1−x

B

+

1+x

C

=>1+3x+2x

2

=A(1−x)(1+x)+B(1−2x)(1+x)+C(1−2x)(1−x)

For x=1,=>1+3(1)+2(1)

2

=A(0)+B(1−2)(1+1)+C(0)

=>6=−2B

=>B=−3 −(1)

For x=−1,=>1+3(−1)+2(−1)

2

=A(0)+B(0)+C(1−2(−1))(1−(−1))

=>0=6C

=>C=0 −(2)

For x=

2

1

,=>1+3(

2

1

)+2(

2

1

)

2

=A(

2

1

)(1+

2

1

)+B(0)+C(0)

=>3=

4

3

A

=>A=4 −(3)

Therefore , from (1),(2) and (3) =>

(1−2x)(1−x)(1+x)

1+3x+2x

2

=

1−2x

4

−

1−x

3