展開する (2x-1)/((ax+b)(cx+d)^2)

解

展開する

\frac{2 x - 1}{( a x + b ) ( c x + d ) ^{2}}

\frac{2 x - 1}{a c ^{2} x ^{3} + 2 a c d x ^{2} + a d ^{2} x + b c ^{2} x ^{2} + 2 b c d x + b d ^{2}}

解答ステップ

\frac{2 x - 1}{( a x + b ) ( c x + d ) ^{2}}

(c x + d)^{2} = c^{2} x^{2} + 2 c d x + d^{2}

= \frac{2 x - 1}{( a x + b ) ( c ^{2} x ^{2} + 2 c d x + d ^{2} )}

拡張

(a x + b) (c^{2} x^{2} + 2 c d x + d^{2}) : a c^{2} x^{3} + 2 a c d x^{2} + a d^{2} x + b c^{2} x^{2} + 2 b c d x + b d^{2}

= \frac{2 x - 1}{a c ^{2} x ^{3} + 2 a c d x ^{2} + a d ^{2} x + b c ^{2} x ^{2} + 2 b c d x + b d ^{2}}