Theory of Intelligence
11TH•Mathematics•Partial Fractions•Question 15

Solution

Resolve into partial fractions: $\dfrac{12x^2-48}{(x-2)^2(x+2)^2}$

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Solution

Let:

12x2−48(x−2)2(x+2)2=Ax−2+B(x−2)2+Cx+2+D(x+2)2\frac{12x^2-48}{(x-2)^2(x+2)^2}=\frac{A}{x-2}+\frac{B}{(x-2)^2}+\frac{C}{x+2}+\frac{D}{(x+2)^2}

Solving gives:

A=3,B=0,C=−3,D=0A=3,\quad B=0,\quad C=-3,\quad D=0

Hence:

12x2−48(x−2)2(x+2)2=3x−2−3x+2\boxed{\frac{12x^2-48}{(x-2)^2(x+2)^2}=\frac{3}{x-2}-\frac{3}{x+2}}

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