Square root of x^2-4 plus x^2/x^2+1

√x² - 4 + x²/x² + 1

x - 2 + x²/x² + 1

x - 2 + x²

1 x² + 1

(x - 2) (x² + 1) + x²

(1) (x² + 1) x² + 1

x³ + x - 2x² - 2 + x²

x² + 1 x² + 1

x³ - 2x² + x² + x - 2

x² + 1

x³ - x² + x - 2

x² + 1

x³ + x - 2