How do you express x2+x(x+2)(x−1)2 in partial fractions?

1 Answer
Narad T.
Jan 17, 2017

The answer is =29x+2+79x−1+23(x−1)2

Explanation:

Let's do the decomposition into partial fractions

x2+x(x+2)(x−1)2=Ax+2+Bx−1+C(x−1)2

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

We equalise the denominators

x2+x=A(x−1)2+B(x+2)(x−1)+C(x+2)

Let x=−2, ⇒,2=9A, ⇒, A=29

Let x=1, ⇒, 2=3C, ⇒, C=23

Coefficients of x2

1=A+B, ⇒, B=1−A=1−29=79

So,

x2+x(x+2)(x−1)2=29x+2+79x−1+23(x−1)2

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