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Find the sum of (x2+1/x-1) and its reciprocal?

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Solution: We have ,

Let $p=fracx^2+1x-1$ , $frac1p=fracx-1x^2+1$

Now , $p+frac1p=fracx^2+1x-1+fracx-1x^2+1=frac(x^2+1)^2+(x-1)^2(x-1)(x^2+1)$

$Rightarrow$ $p+frac1p=fracx^4+3x^2-2x+2(x-1)(x^2+1).$

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Deependra Verma

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