Question

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

Answer 1

$x^{2} + \frac{1}{x}-1= \frac{x^3+1-x}{x}= \frac{x^3-x+1}{x} \\ \\reciprocal=\frac{x}{x^3-x+1}\\ \\sum=\frac{x^3-x+1}{x}+\frac{x}{x^3-x+1}\\ \\sum= \frac{(x^3-x+1)^2+ x^{2} }{x(x^3-x+1)} \\ \\sum= \frac{(x^6+ x^{2} +1-2x^4+2x^3-2x)+ x^{2} }{x(x^3-x+1)} \\ \\sum=\frac{x^6- 2x^{4} +2x^3+2 x^{2} -2x+1}{x(x^3-x+1)}$