\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}-\frac{4 x}{x^{2}+1}\right)+\frac – InterviewSolution

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1.

\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}-\frac{4 x}{x^{2}+1}\right)+\frac{4 x}{x^{4}-1}

Answer»

(x+1)/(x-1) - (x-1)/(x+1) =(x^2+2x+1-x^2+2x-1)/(x^2-1)=(4x)/(x^2-1)

4x/(x^2-1) - 4x/(x^2+1) =(4x^3+4x-4x^3+4x)/(x^4-1)=8x/(x^4-1)

(8x/(x^4-1))/((4x)/(x^4-1))=2

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