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.

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