euclidean division of x^4+x^2-1 by x^2+1

Perform the Euclidean division of

(x^{4} + x^{2} - 1)

(x^{2} + 1)

Current expression	Divide leading terms	Quotient	Quotient × divisor	Remainder after subtracting
$x^{4} + x^{2} - 1$	$\frac{x^{4}}{x^{2}}$	$x^{2}$	$x^{2} \cdot (x^{2} + 1) = x^{4} + x^{2}$	$(x^{4} + x^{2} - 1) - (x^{4} + x^{2}) = -1$

Therefore, the result of the Euclidean division is:

x^{2}

▶Result of the division:

x^{2} - \frac{1}{x^{2} + 1}

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