Theory of Intelligence
11TH•Mathematics•Partial Fractions•Question 7

Solution

Resolve into partial fractions: $\dfrac{3x^2-12x+11}{(x-1)(x-2)(x-3)}$

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Solution

Let:

3x2−12x+11(x−1)(x−2)(x−3)=Ax−1+Bx−2+Cx−3\frac{3x^2-12x+11}{(x-1)(x-2)(x-3)} =\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}

Solving gives A=1A=1, B=1B=1, C=1C=1.

3x2−12x+11(x−1)(x−2)(x−3)=1x−1+1x−2+1x−3\boxed{\frac{3x^2-12x+11}{(x-1)(x-2)(x-3)}=\frac{1}{x-1}+\frac{1}{x-2}+\frac{1}{x-3}}

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