展开 (2x^2+2x+13)/((x-2)(x^2+1)^2)

解答

展开

\frac{2 x ^{2} + 2 x + 13}{( x - 2 ) ( x ^{2} + 1 ) ^{2}}

\frac{2 x ^{2} + 2 x + 13}{x ^{5} + 2 x ^{3} + x - 2 x ^{4} - 4 x ^{2} - 2}

求解步骤

\frac{2 x ^{2} + 2 x + 13}{( x - 2 ) ( x ^{2} + 1 ) ^{2}}

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

= \frac{2 x ^{2} + 2 x + 13}{( x - 2 ) ( x ^{4} + 2 x ^{2} + 1 )}

乘开

(x - 2) (x^{4} + 2 x^{2} + 1) : x^{5} + 2 x^{3} + x - 2 x^{4} - 4 x^{2} - 2

= \frac{2 x ^{2} + 2 x + 13}{x ^{5} + 2 x ^{3} + x - 2 x ^{4} - 4 x ^{2} - 2}

e x p an d \frac{s ^{2} + 7}{( s - 2 ) ^{2} ( s ^{2} + 10 s + 50 )}

s im pl i f y - y^{2} (y - x^{4} - \frac{y ^{4}}{4})

e x p an d (x - 4) (a x - 2 + 3 x - 6)

e x p an d sin (π (2 n - 1))

s im pl i f y (5 - 4 z i)^{2}