展開する (4(x^2-4x-1))/((x-1)^2(x+3)^2)

解

展開する

\frac{4 ( x ^{2} - 4 x - 1 )}{( x - 1 ) ^{2} ( x + 3 ) ^{2}}

\frac{4 x ^{2} - 16 x - 4}{x ^{4} + 4 x ^{3} - 2 x ^{2} - 12 x + 9}

解答ステップ

\frac{4 ( x ^{2} - 4 x - 1 )}{( x - 1 ) ^{2} ( x + 3 ) ^{2}}

(x - 1)^{2} = x^{2} - 2 x + 1

= \frac{4 ( x ^{2} - 4 x - 1 )}{( x ^{2} - 2 x + 1 ) ( x + 3 ) ^{2}}

(x + 3)^{2} = x^{2} + 6 x + 9

= \frac{4 ( x ^{2} - 4 x - 1 )}{( x ^{2} - 2 x + 1 ) ( x ^{2} + 6 x + 9 )}

拡張

(x^{2} - 2 x + 1) (x^{2} + 6 x + 9) : x^{4} + 4 x^{3} - 2 x^{2} - 12 x + 9

= \frac{4 ( x ^{2} - 4 x - 1 )}{x ^{4} + 4 x ^{3} - 2 x ^{2} - 12 x + 9}

拡張

4 (x^{2} - 4 x - 1) : 4 x^{2} - 16 x - 4

= \frac{4 x ^{2} - 16 x - 4}{x ^{4} + 4 x ^{3} - 2 x ^{2} - 12 x + 9}