erweitern (2(x+5)^2)/((x^2+2)^2)

Lösung

erweitern

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

\frac{2 x ^{2} + 20 x + 50}{x ^{4} + 4 x ^{2} + 4}

Schritte zur Lösung

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

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

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

(x + 5)^{2} = x^{2} + 10 x + 25

= \frac{2 ( x ^{2} + 10 x + 25 )}{x ^{4} + 4 x ^{2} + 4}

Multipliziere aus

2 (x^{2} + 10 x + 25) : 2 x^{2} + 20 x + 50

= \frac{2 x ^{2} + 20 x + 50}{x ^{4} + 4 x ^{2} + 4}

e x p an d \frac{15 x ^{2} + 24 x - 25}{( 5 x + 4 ) ^{2}}

e x p an d \frac{( x + 6 ) ( x + 2 )}{( x - 3 ) ( x - 2 )}

e x p an d 4 (e^{3 x + 1} + \frac{7}{x}) + ln (3 (e^{3 x + 1} + \frac{7}{x}) + 2)

e x p an d \frac{( 1 + 2 x )}{( 3 x - 1 ) ^{3}}

e x p an d \frac{22 ( 29 x - 144 )}{3}