簡約 (x-(24)/(x+2))(x-(12)/(x-4))

解

簡約

(x - \frac{24}{x + 2}) (x - \frac{12}{x - 4})

(x + 6) (x - 6)

解答ステップ

(x - \frac{24}{x + 2}) (x - \frac{12}{x - 4})

結合

x - \frac{24}{x + 2} : \frac{x ^{2} + 2 x - 24}{x + 2}

= \frac{x ^{2} + 2 x - 24}{x + 2} (x - \frac{12}{x - 4})

分数の規則を適用する:

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

= \frac{( x ^{2} + 2 x - 24 ) ( x - \frac{12}{x - 4} )}{x + 2}

簡素化

(x^{2} + 2 x - 24) (x - \frac{12}{x - 4}) : (x + 6) (x^{2} - 4 x - 12)

= \frac{( x + 6 ) ( x ^{2} - 4 x - 12 )}{x + 2}

因数

x^{2} - 4 x - 12 : (x + 2) (x - 6)

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

共通因数を約分する:

x + 2

= (x + 6) (x - 6)