Question

Resolve into Partial functions 1 / x²-x-6
​

Answer 1

Answer:

This is the answer

Step-by-step explanation:

The first thing is to factor the denominator and get the form of the partial fraction decomposition

⇒

(x

2

+1)(x+5)

26x

2

+208x

=

x

2

+1

Ax+B

+

x+5

C

The next step is to set numerators equal

⇒26x

2

+208x=(Ax+B)(x+5)+C(x

2

+1)

⇒26x

2

+208x=(A+C)x

2

−x(5A+B)+(5B+C)

we can just pick a few values of x and find the constants so let’s do that

⇒ x=0 5B+C=0.....................(1)

⇒ x=1 2C+6A+6B=234...........(2)

⇒ x=−1 2C−4A+4B=−182......(3)

Now, by solving eq 1,2,3, we get

A=41, B=3, C=−15

⇒

(x

2

+1)(x+5)

26x

2

+208

=

x

2

+1

41x+3

−

x+5

15