簡約 (x+1)(x-4)(x+1/2)(x-4/3)

解

簡約

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

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

解答ステップ

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

簡素化

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

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

分数の規則を適用する:

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

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

簡素化

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

= \frac{\frac{( x + 1 ) ( x - 4 ) ( 2 x + 1 ) ( x \cdot 3 - 4 )}{3}}{2}

分数の規則を適用する:

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

= \frac{( x + 1 ) ( x - 4 ) ( 2 x + 1 ) ( x \cdot 3 - 4 )}{3 \cdot 2}

数を乗じる:

3 \cdot 2 = 6

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

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