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

Lösung

erweitern

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

\frac{x ^{2} + 4 x + 1}{x ^{4} + 2 x ^{2} - 2 x ^{3} - 2 x + 1}

Schritte zur Lösung

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

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

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

Multipliziere aus

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

= \frac{x ^{2} + 4 x + 1}{x ^{4} + 2 x ^{2} - 2 x ^{3} - 2 x + 1}

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

e x p an d \frac{( 4 x - 3 ) ^{2}}{16}

e x p an d - e^{θ} (- e^{- θ} θ - e^{- θ})

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

e x p an d (4 k - m x) (k b^{2} - \frac{m b ^{2}}{4} x)