簡約 (\frac{x^2-6x-16)/(x^2+4x-21)}{(x^2+9x+14)/(x^2-8x+15)}

解

簡約

\frac{\frac{x ^{2} - 6 x - 16}{x ^{2} + 4 x - 21}}{\frac{x ^{2} + 9 x + 14}{x ^{2} - 8 x + 15}}

\frac{( x - 8 ) ( x - 5 )}{( x + 7 ) ^{2}}

解答ステップ

\frac{\frac{x ^{2} - 6 x - 16}{x ^{2} + 4 x - 21}}{\frac{x ^{2} + 9 x + 14}{x ^{2} - 8 x + 15}}

分数の規則を適用する:

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

= \frac{( x ^{2} - 6 x - 16 ) ( x ^{2} - 8 x + 15 )}{( x ^{2} + 4 x - 21 ) ( x ^{2} + 9 x + 14 )}

キャンセル

\frac{( x ^{2} - 6 x - 16 ) ( x ^{2} - 8 x + 15 )}{( x ^{2} + 4 x - 21 ) ( x ^{2} + 9 x + 14 )} : \frac{( x - 8 ) ( x - 5 )}{( x + 7 ) ^{2}}

= \frac{( x - 8 ) ( x - 5 )}{( x + 7 ) ^{2}}