簡約 (x^2+4x-12)/(x^2(x^2+9x+18))*6x^2

解

簡約

\frac{x ^{2} + 4 x - 12}{x ^{2} ( x ^{2} + 9 x + 18 )} \cdot 6 x^{2}

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

解答ステップ

\frac{x ^{2} + 4 x - 12}{x ^{2} ( x ^{2} + 9 x + 18 )} \cdot 6 x^{2}

キャンセル

\frac{x ^{2} + 4 x - 12}{x ^{2} ( x ^{2} + 9 x + 18 )} : \frac{x - 2}{x ^{2} ( x + 3 )}

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

分数の規則を適用する:

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

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

共通因数を約分する:

x^{2}

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

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