展開する (7x+2)/((x-4)^2(x^2+5x+4)(x^2+x+5)^2)

解

展開する

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

\frac{7 x + 2}{x ^{8} - x ^{7} - 15 x ^{6} - 15 x ^{5} - 65 x ^{4} + 381 x ^{3} + 684 x ^{2} + 1840 x + 1600}

解答ステップ

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

(x - 4)^{2} = x^{2} - 8 x + 16

= \frac{7 x + 2}{( x ^{2} - 8 x + 16 ) ( x ^{2} + 5 x + 4 ) ( x ^{2} + x + 5 ) ^{2}}

(x^{2} + x + 5)^{2} = x^{4} + 2 x^{3} + 11 x^{2} + 10 x + 25

= \frac{7 x + 2}{( x ^{2} - 8 x + 16 ) ( x ^{2} + 5 x + 4 ) ( x ^{4} + 2 x ^{3} + 11 x ^{2} + 10 x + 25 )}

拡張

(x^{2} - 8 x + 16) (x^{2} + 5 x + 4) (x^{4} + 2 x^{3} + 11 x^{2} + 10 x + 25) : x^{8} - x^{7} - 15 x^{6} - 15 x^{5} - 65 x^{4} + 381 x^{3} + 684 x^{2} + 1840 x + 1600

= \frac{7 x + 2}{x ^{8} - x ^{7} - 15 x ^{6} - 15 x ^{5} - 65 x ^{4} + 381 x ^{3} + 684 x ^{2} + 1840 x + 1600}