vereinfachen (2(5/12))/(1-(5/12)^2)

Lösung

vereinfachen

\frac{2 ( \frac{5}{12} )}{1 - ( \frac{5}{12} ) ^{2}}

\frac{120}{119}

Dezimale

1.00840 \dots

Schritte zur Lösung

\frac{2 ( \frac{5}{12} )}{1 - ( \frac{5}{12} ) ^{2}}

Apply rule:

(a) = a

(\frac{5}{12}) = \frac{5}{12}

= \frac{2 \cdot \frac{5}{12}}{1 - ( \frac{5}{12} ) ^{2}}

2 \cdot \frac{5}{12} = \frac{5}{6}

= \frac{\frac{5}{6}}{1 - ( \frac{5}{12} ) ^{2}}

Vereinfache

1 - (\frac{5}{12})^{2} : \frac{119}{144}

= \frac{\frac{5}{6}}{\frac{119}{144}}

Wende Bruchregel an:

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

= \frac{5 \cdot 144}{6 \cdot 119}

Streiche

\frac{5 \cdot 144}{6 \cdot 119} : \frac{120}{119}

= \frac{120}{119}

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