展开 (5x^2+6x+9)/((x-3)^2*(x+1)^2)

解答

展开

\frac{5 x ^{2} + 6 x + 9}{( x - 3 ) ^{2} \cdot ( x + 1 ) ^{2}}

\frac{5 x ^{2} + 6 x + 9}{x ^{4} - 4 x ^{3} - 2 x ^{2} + 12 x + 9}

求解步骤

\frac{5 x ^{2} + 6 x + 9}{( x - 3 ) ^{2} ( x + 1 ) ^{2}}

(x - 3)^{2} = x^{2} - 6 x + 9

= \frac{5 x ^{2} + 6 x + 9}{( x ^{2} - 6 x + 9 ) ( x + 1 ) ^{2}}

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

= \frac{5 x ^{2} + 6 x + 9}{( x ^{2} - 6 x + 9 ) ( x ^{2} + 2 x + 1 )}

乘开

(x^{2} - 6 x + 9) (x^{2} + 2 x + 1) : x^{4} - 4 x^{3} - 2 x^{2} + 12 x + 9

= \frac{5 x ^{2} + 6 x + 9}{x ^{4} - 4 x ^{3} - 2 x ^{2} + 12 x + 9}

e x p an d \frac{2 n}{( 1 - x ) ^{2}}

e x p an d (tan (z) - sin (x) sin (y)) d x + cos (x) cos (y) d y

e x p an d \frac{( x ^{2} + 15 )}{( x + 5 ) ^{2} ( x ^{2} + 5 )}

s im pl i f y (2 + 2 i)^{7}

e x p an d - \frac{3 x ( x - 8 )}{8}