vereinfachen (x+sqrt(x^2+1))^2

Lösung

vereinfachen

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

2 x^{2} + 2 x x^{2} + 1 + 1

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

Vereinfache

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

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

s im pl i f y (1 + cos^{2} (x)) (tan (x))

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

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

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

e x p an d (cos (2 π t) - 2 π t sin (2 π t))^{2}