vereinfachen (x+(1/x))*(1+2/(x^2-1))

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

Füge zusammen:

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

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

Wende Bruchregel an:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Vereinfache

(x + \frac{1}{x}) (x^{2} + 1) : \frac{( x ^{2} + 1 ) ^{2}}{x}

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

Wende Bruchregel an:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

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

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s im pl i f y (3 - x) (2 - x)

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e x p an d \frac{1}{4 ( - 16 x + 8 )}