Express X/((X+1)(X+2)) in partial fractions. OCR C4 style question

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=-1The second bracket is cancelled out and so we are left with:-1=AAndX=-2The first bracket is cancelled out and so we are left with:B=2Putting 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.