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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

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

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

Streiche

\frac{x ^{2} x ^{2} - 4}{x ^{2}} : x^{2} - 4

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

e x p an d (x - \frac{2}{3})^{8}

e x p an d \frac{8 x - 2}{( x - 1 ) ^{2} ( x + 2 )}

e x p an d sin^{2} (2 x) \cdot (cot^{2} (x) - tan^{2} (x))

e x p an d \frac{( s - 1 ) \cdot ( s + 7 )}{( s + 1 ) \cdot ( s - 2 ) \cdot ( s + 3 )}

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