簡約 2(x+1/3)(x+1/5)(x+1/4)(x+1/2)

解

簡約

2 (x + \frac{1}{3}) (x + \frac{1}{5}) (x + \frac{1}{4}) (x + \frac{1}{2})

\frac{( 3 x + 1 ) ( 5 x + 1 ) ( 4 x + 1 ) ( 2 x + 1 )}{60}

解答ステップ

2 (x + \frac{1}{3}) (x + \frac{1}{5}) (x + \frac{1}{4}) (x + \frac{1}{2})

簡素化

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

= 2 \cdot \frac{3 x + 1}{3} (x + \frac{1}{5}) (x + \frac{1}{4}) (x + \frac{1}{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 + 1 ) ( x + \frac{1}{5} ) ( x + \frac{1}{4} ) ( x + \frac{1}{2} )}{3}

簡素化

2 (3 x + 1) (x + \frac{1}{5}) (x + \frac{1}{4}) (x + \frac{1}{2}) : \frac{( 3 x + 1 ) ( x \cdot 5 + 1 ) ( x \cdot 4 + 1 ) ( x \cdot 2 + 1 )}{20}

= \frac{\frac{( 3 x + 1 ) ( x \cdot 5 + 1 ) ( x \cdot 4 + 1 ) ( x \cdot 2 + 1 )}{20}}{3}

分数の規則を適用する:

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

= \frac{( 3 x + 1 ) ( x \cdot 5 + 1 ) ( x \cdot 4 + 1 ) ( x \cdot 2 + 1 )}{20 \cdot 3}

数を乗じる:

20 \cdot 3 = 60

= \frac{( 3 x + 1 ) ( x \cdot 5 + 1 ) ( x \cdot 4 + 1 ) ( x \cdot 2 + 1 )}{60}

= \frac{( 3 x + 1 ) ( 5 x + 1 ) ( 4 x + 1 ) ( 2 x + 1 )}{60}