How do you express 4x2−7x−12(x)(x+2)(x−3) in partial fractions?

2 Answers
Narad T.
Dec 16, 2016

The answer is =2x+95x+2+15x−3

Explanation:

Let's do the decomposition into partial fractions

4x2−7x−12x(x+2)(x−3)=Ax+Bx+2+Cx−3

=A(x+2)(x−3)+B(x)(x−3)+C(x)(x+2)x(x+2)(x−3)

Therefore,

4x2−7x−12=A(x+2)(x−3)+B(x)(x−3)+C(x)(x+2)

Let x=0, ⇒, −12=−6A, ⇒, A=2

Let x=−2,⇒, 18=10B, ⇒, B=95

Let x=3, ⇒, 3=15C, ⇒, C=15

So,

4x2−7x−12x(x+2)(x−3)=2x+95x+2+15x−3

Shwetank Mauria
Dec 16, 2016

4x2−7x−12x(x+2)(x−3)=2x+95(x+2)+15(x−3)

Explanation:

Let 4x2−7x−12x(x+2)(x−3)⇔Ax+Bx+2+Cx−3

Hence 4x2−7x−12x(x+2)(x−3)⇔A(x+2)(x−3)+Bx(x−3)+Cx(x+2)x(x+2)(x−3)

i.e. 4x2−7x−12⇔A(x+2)(x−3)+Bx(x−3)+Cx(x+2)

Now putting x=0, we get −6A=−12 or A=2

putting x=3, we get 15C=3 or C=15

and putting x=−2, we get 10B=16+14−12=18 or B=95

Hence 4x2−7x−12x(x+2)(x−3)=2x+95(x+2)+15(x−3)

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