簡約 (-(4/3)^2+2(8/3))/((8/3)^2-2(4/3))

解

簡約

\frac{- ( \frac{4}{3} ) ^{2} + 2 ( \frac{8}{3} )}{( \frac{8}{3} ) ^{2} - 2 ( \frac{4}{3} )}

\frac{4}{5}

十進法表記

0.8

解答ステップ

\frac{- ( \frac{4}{3} ) ^{2} + 2 ( \frac{8}{3} )}{( \frac{8}{3} ) ^{2} - 2 ( \frac{4}{3} )}

\frac{- ( \frac{4}{3} ) ^{2} + 2 ( \frac{8}{3} )}{( \frac{8}{3} ) ^{2} - 2 ( \frac{4}{3} )} = \frac{- ( \frac{4}{3} ) ^{2} + 2 \cdot \frac{8}{3}}{( \frac{8}{3} ) ^{2} - 2 \cdot \frac{4}{3}}

= \frac{- ( \frac{4}{3} ) ^{2} + 2 \cdot \frac{8}{3}}{( \frac{8}{3} ) ^{2} - 2 \cdot \frac{4}{3}}

- (\frac{4}{3})^{2} + 2 \cdot \frac{8}{3} = \frac{32}{9}

= \frac{\frac{32}{9}}{( \frac{8}{3} ) ^{2} - 2 \cdot \frac{4}{3}}

(\frac{8}{3})^{2} - 2 \cdot \frac{4}{3} = \frac{40}{9}

= \frac{\frac{32}{9}}{\frac{40}{9}}

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{32 \cdot 9}{9 \cdot 40}

キャンセル

\frac{32 \cdot 9}{9 \cdot 40} : \frac{4}{5}

= \frac{4}{5}