Question

How do you use partial fraction decomposition to decompose the fraction to integrate `(3x)/((x + 2)(x - 1))`?

Answer 1

The required format in partial fraction is`2/(x+2) + 1/(x-1)`

Explanation:

Let us consider two constants A and B such that `A/(x+2) + B/(x-1)`
Now taking L.C.M we get
`(A(x-1)+B(x+2))/((x-1)(x+2)) = 3x/((x+2)(x-1))`
Comparing the numerators we get
`(A(x-1)+B(x+2))=3x`
Now putting x=1 we get
B=1
And putting x=-2 we get
A=2
So required form is
`2/(x+2) + 1/(x-1)`

Hope it helps!!