展開する-(2(2x-7))/((x-2)^2(x-5)^2)

解

展開する

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

- \frac{4 x - 14}{x ^{4} - 14 x ^{3} + 69 x ^{2} - 140 x + 100}

解答ステップ

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

(x - 2)^{2} = x^{2} - 4 x + 4

= - \frac{2 ( 2 x - 7 )}{( x ^{2} - 4 x + 4 ) ( x - 5 ) ^{2}}

(x - 5)^{2} = x^{2} - 10 x + 25

= - \frac{2 ( 2 x - 7 )}{( x ^{2} - 4 x + 4 ) ( x ^{2} - 10 x + 25 )}

拡張

(x^{2} - 4 x + 4) (x^{2} - 10 x + 25) : x^{4} - 14 x^{3} + 69 x^{2} - 140 x + 100

= - \frac{2 ( 2 x - 7 )}{x ^{4} - 14 x ^{3} + 69 x ^{2} - 140 x + 100}

拡張

2 (2 x - 7) : 4 x - 14

= - \frac{4 x - 14}{x ^{4} - 14 x ^{3} + 69 x ^{2} - 140 x + 100}