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

Answers (1)

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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