展開する (30(x^2+3))/((x-3)^3(x+3)^3)

解

展開する

\frac{30 ( x ^{2} + 3 )}{( x - 3 ) ^{3} ( x + 3 ) ^{3}}

\frac{30 x ^{2} + 90}{x ^{6} - 27 x ^{4} + 243 x ^{2} - 729}

解答ステップ

\frac{30 ( x ^{2} + 3 )}{( x - 3 ) ^{3} ( x + 3 ) ^{3}}

(x - 3)^{3} = x^{3} - 9 x^{2} + 27 x - 27

= \frac{30 ( x ^{2} + 3 )}{( x ^{3} - 9 x ^{2} + 27 x - 27 ) ( x + 3 ) ^{3}}

(x + 3)^{3} = x^{3} + 9 x^{2} + 27 x + 27

= \frac{30 ( x ^{2} + 3 )}{( x ^{3} - 9 x ^{2} + 27 x - 27 ) ( x ^{3} + 9 x ^{2} + 27 x + 27 )}

拡張

(x^{3} - 9 x^{2} + 27 x - 27) (x^{3} + 9 x^{2} + 27 x + 27) : x^{6} - 27 x^{4} + 243 x^{2} - 729

= \frac{30 ( x ^{2} + 3 )}{x ^{6} - 27 x ^{4} + 243 x ^{2} - 729}

拡張

30 (x^{2} + 3) : 30 x^{2} + 90

= \frac{30 x ^{2} + 90}{x ^{6} - 27 x ^{4} + 243 x ^{2} - 729}