erweitern ((t^2+3)^2)/(t^6)

Lösung

erweitern

\frac{( t ^{2} + 3 ) ^{2}}{t ^{6}}

\frac{1}{t ^{2}} + \frac{6}{t ^{4}} + \frac{9}{t ^{6}}

Schritte zur Lösung

\frac{( t ^{2} + 3 ) ^{2}}{t ^{6}}

(t^{2} + 3)^{2} = t^{4} + 6 t^{2} + 9

= \frac{t ^{4} + 6 t ^{2} + 9}{t ^{6}}

Wende Bruchregel an:

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

\frac{t ^{4} + 6 t ^{2} + 9}{t ^{6}} = \frac{t ^{4}}{t ^{6}} + \frac{6 t ^{2}}{t ^{6}} + \frac{9}{t ^{6}}

= \frac{t ^{4}}{t ^{6}} + \frac{6 t ^{2}}{t ^{6}} + \frac{9}{t ^{6}}

Streiche

\frac{t ^{4}}{t ^{6}} : \frac{1}{t ^{2}}

= \frac{1}{t ^{2}} + \frac{6 t ^{2}}{t ^{6}} + \frac{9}{t ^{6}}

Streiche

\frac{6 t ^{2}}{t ^{6}} : \frac{6}{t ^{4}}

= \frac{1}{t ^{2}} + \frac{6}{t ^{4}} + \frac{9}{t ^{6}}

e x p an d sin (x (1 + csc (x)) - sin (x))

e x p an d (w + x + y + z + 1)^{3}

e x p an d \frac{x ( x - 5 )}{2}

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

e x p an d \frac{x + 3}{( x - 1 ) ( x - 5 )}