확장 (x^4+5x^2+2)/(x^2(x^2+1)^2)

해법

확장

\frac{x ^{4} + 5 x ^{2} + 2}{x ^{2} ( x ^{2} + 1 ) ^{2}}

\frac{x ^{4} + 5 x ^{2} + 2}{x ^{6} + 2 x ^{4} + x ^{2}}

솔루션 단계

\frac{x ^{4} + 5 x ^{2} + 2}{x ^{2} ( x ^{2} + 1 ) ^{2}}

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

= \frac{x ^{4} + 5 x ^{2} + 2}{x ^{2} ( x ^{4} + 2 x ^{2} + 1 )}

x^{2} (x^{4} + 2 x^{2} + 1)

확대한다:

x^{6} + 2 x^{4} + x^{2}

= \frac{x ^{4} + 5 x ^{2} + 2}{x ^{6} + 2 x ^{4} + x ^{2}}