展開する (5x^2+6x+9)/((x-3)^2(x+1)^2)

解

展開する

\frac{5 x ^{2} + 6 x + 9}{( x - 3 ) ^{2} ( x + 1 ) ^{2}}

\frac{5 x ^{2} + 6 x + 9}{x ^{4} - 4 x ^{3} - 2 x ^{2} + 12 x + 9}

解答ステップ

\frac{5 x ^{2} + 6 x + 9}{( x - 3 ) ^{2} ( x + 1 ) ^{2}}

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

= \frac{5 x ^{2} + 6 x + 9}{( x ^{2} - 6 x + 9 ) ( x + 1 ) ^{2}}

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

= \frac{5 x ^{2} + 6 x + 9}{( x ^{2} - 6 x + 9 ) ( x ^{2} + 2 x + 1 )}

拡張

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

= \frac{5 x ^{2} + 6 x + 9}{x ^{4} - 4 x ^{3} - 2 x ^{2} + 12 x + 9}