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

Lösung

erweitern

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

\frac{4 x ^{2} + 2 x}{x ^{4} - 2 x ^{2} + 1}

Schritte zur Lösung

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

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

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

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

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

Multipliziere aus

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

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

e x p an d \frac{4 x - 28}{3 ( x + 2 ) ( x - 5 )}

e x p an d (x - 2)^{5} (x + 2)^{6} x^{4}

e x p an d \frac{- 10 + 2 x ^{2}}{x ( 1 + x ^{2} ) ( 4 + x ^{2} )}

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

e x p an d 4 (3 m^{2} - 7 m + 2)^{2}