簡約 (1/3+x/2)(1/9-(x^2)/4)(1/3-x/2)

解

簡約

(\frac{1}{3} + \frac{x}{2}) (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2})

\frac{( 2 + 3 x ) ( 4 - 9 x ^{2} ) ( 2 - 3 x )}{1296}

解答ステップ

(\frac{1}{3} + \frac{x}{2}) (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2})

簡素化

\frac{1}{3} + \frac{x}{2} : \frac{2 + 3 x}{6}

= \frac{2 + 3 x}{6} (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2})

分数の規則を適用する:

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

= \frac{( 2 + 3 x ) ( \frac{1}{9} - \frac{x ^{2}}{4} ) ( \frac{1}{3} - \frac{x}{2} )}{6}

簡素化

(2 + 3 x) (\frac{1}{9} - \frac{x ^{2}}{4}) (\frac{1}{3} - \frac{x}{2}) : \frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{216}

= \frac{\frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{216}}{6}

分数の規則を適用する:

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

= \frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{216 \cdot 6}

数を乗じる:

216 \cdot 6 = 1296

= \frac{( 2 + 3 x ) ( 4 - x ^{2} \cdot 9 ) ( 2 - x \cdot 3 )}{1296}

= \frac{( 2 + 3 x ) ( 4 - 9 x ^{2} ) ( 2 - 3 x )}{1296}