展開する x/((x-a)^2(x-b)^2)

解

展開する

\frac{x}{( x - a ) ^{2} ( x - b ) ^{2}}

\frac{x}{x ^{4} - 2 b x ^{3} + b ^{2} x ^{2} - 2 a x ^{3} + 4 ab x ^{2} - 2 a b ^{2} x + a ^{2} x ^{2} - 2 a ^{2} b x + a ^{2} b ^{2}}

解答ステップ

\frac{x}{( x - a ) ^{2} ( x - b ) ^{2}}

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

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

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

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

拡張

(x^{2} - 2 x a + a^{2}) (x^{2} - 2 x b + b^{2}) : x^{4} - 2 b x^{3} + b^{2} x^{2} - 2 a x^{3} + 4 ab x^{2} - 2 a b^{2} x + a^{2} x^{2} - 2 a^{2} b x + a^{2} b^{2}

= \frac{x}{x ^{4} - 2 b x ^{3} + b ^{2} x ^{2} - 2 a x ^{3} + 4 ab x ^{2} - 2 a b ^{2} x + a ^{2} x ^{2} - 2 a ^{2} b x + a ^{2} b ^{2}}