Theory of Intelligence
11TH•Mathematics•Partial Fractions•Question 3

Solution

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

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Solution

x2+1(x+1)(x−1)\frac{x^2+1}{(x+1)(x-1)}

First make it a mixed form:

x2+1x2−1=1+2x2−1\frac{x^2+1}{x^2-1}=1+\frac{2}{x^2-1}

Now:

2x2−1=1x−1−1x+1\frac{2}{x^2-1}=\frac{1}{x-1}-\frac{1}{x+1}

Hence:

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

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