This question is asking us to split up the fraction into two separate fractions.

To begin we use one of the standard forms for solving partial fractions, this is (A/(X+1))+(B/(X+2)).

To solve set the first equation equal to the standard form and then solve as shown below.

X/((X+1)(X+2)= (A/(X+1))+(B/(X+2))

X=A(X+2)+B(X+1)

We can solve this equation by substituting in values for X, shown below:

X=-1

The second bracket is cancelled out and so we are left with:

-1=A

And

X=-2

The first bracket is cancelled out and so we are left with:

B=2

Putting all of this back together gives:

(2/(X+2)) –(1(X+1))

Apologies for the style of the equations the website currently doesn’t support words equation editor.