Warum gilt \frac{x^{2n}}{1+x^{2n}} -1 = \frac{1}{1+x^{2n}}?

Question

Aufgabe:

Warum ist \( |\frac{x^{2n}}{1+x^{2n}} -1| = \frac{1}{1+x^{2n}}  \)?

Problem/Ansatz:

Wie schaut die Umformung aus?

Answer 1

\( |\frac{x^{2n}}{1+x^{2n}} -1| \)

\( =|\frac{x^{2n}}{1+x^{2n}} -\frac{1+x^{2n}}{1+x^{2n}} | \)

\( =| \frac{-1}{1+x^{2n}}  | \)

\( = \frac{1}{1+x^{2n}}  \)