簡約 (2(12/5))/(1-(12/5)^2)

解

簡約

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

- \frac{120}{119}

十進法表記

- 1.00840 \dots

解答ステップ

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

規則を適用する:

(a) = a

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

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

2 \cdot \frac{12}{5} = \frac{24}{5}

= \frac{\frac{24}{5}}{1 - ( \frac{12}{5} ) ^{2}}

簡素化

1 - (\frac{12}{5})^{2} : - \frac{119}{25}

= \frac{\frac{24}{5}}{- \frac{119}{25}}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{24}{5}}{\frac{119}{25}}

分数の規則を適用する:

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

\frac{\frac{24}{5}}{\frac{119}{25}} = \frac{24 \cdot 25}{5 \cdot 119}

= - \frac{24 \cdot 25}{5 \cdot 119}

キャンセル

- \frac{24 \cdot 25}{5 \cdot 119} : - \frac{120}{119}

= - \frac{120}{119}