erweitern (x^4+x^2+1)/((x^2+3x+2)^2(x+4)^2)

Lösung

erweitern

\frac{x ^{4} + x ^{2} + 1}{( x ^{2} + 3 x + 2 ) ^{2} ( x + 4 ) ^{2}}

\frac{x ^{4} + x ^{2} + 1}{x ^{6} + 14 x ^{5} + 77 x ^{4} + 212 x ^{3} + 308 x ^{2} + 224 x + 64}

Schritte zur Lösung

\frac{x ^{4} + x ^{2} + 1}{( x ^{2} + 3 x + 2 ) ^{2} ( x + 4 ) ^{2}}

(x^{2} + 3 x + 2)^{2} = x^{4} + 6 x^{3} + 13 x^{2} + 12 x + 4

= \frac{x ^{4} + x ^{2} + 1}{( x ^{4} + 6 x ^{3} + 13 x ^{2} + 12 x + 4 ) ( x + 4 ) ^{2}}

(x + 4)^{2} = x^{2} + 8 x + 16

= \frac{x ^{4} + x ^{2} + 1}{( x ^{4} + 6 x ^{3} + 13 x ^{2} + 12 x + 4 ) ( x ^{2} + 8 x + 16 )}

Multipliziere aus

(x^{4} + 6 x^{3} + 13 x^{2} + 12 x + 4) (x^{2} + 8 x + 16) : x^{6} + 14 x^{5} + 77 x^{4} + 212 x^{3} + 308 x^{2} + 224 x + 64

= \frac{x ^{4} + x ^{2} + 1}{x ^{6} + 14 x ^{5} + 77 x ^{4} + 212 x ^{3} + 308 x ^{2} + 224 x + 64}

e x p an d (x^{3} + y^{3}) d x - x y^{2} d y

e x p an d - y l e f t (x - y)

e x p an d \frac{3}{x ( x - 2 )}

e x p an d \frac{x}{7 ( x - 2 ) ( x + 6 )}

e x p an d \frac{7 s ^{2} - 15 s + 75}{s ( s ^{2} + 25 )}