Express (X²-16)/(X-1)(X+3) in partial fractions

(X²-16)/(X-1)(X+3) can be expressed as partial fractions as it is equivalent to A + B/(X-1) + C/(X+3) giving us : (X²-16)/(X-1)(X+3)≡ A + B/(X-1) +C/X+3). By multiplying both sides of this equation by (X-1) and (X+3) you get X²-16≡A(X-1)(X+3) + B(X+3) +C(X-1). This must be true for all values so to work out the variables A, B and C you start off by looking at the values of X which make the value of the bracket 0. These are X=1 and X=-3. When X=1: -15=4B, therefore B=-15/4. When X=-3: -7=-4C, therefore C=7/4. When the brackets are fully expanded the only X² term is AX² , therefore AX²=X², therefore A=1.