簡約 (x^2+1/4)(x^2+1/5)

解

簡約

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

\frac{( 4 x ^{2} + 1 ) ( 5 x ^{2} + 1 )}{20}

解答ステップ

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

簡素化

x^{2} + \frac{1}{4} : \frac{4 x ^{2} + 1}{4}

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

分数の規則を適用する:

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

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

簡素化

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

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

分数の規則を適用する:

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

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

数を乗じる:

5 \cdot 4 = 20

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

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