erweitern (x^2+(y-1)^2)/(x^2)

Lösung

erweitern

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

1 + \frac{y ^{2}}{x ^{2}} - \frac{2 y}{x ^{2}} + \frac{1}{x ^{2}}

Schritte zur Lösung

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

Multipliziere aus

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

= \frac{x ^{2} + y ^{2} - 2 y + 1}{x ^{2}}

Wende Bruchregel an:

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

\frac{x ^{2} + y ^{2} - 2 y + 1}{x ^{2}} = \frac{x ^{2}}{x ^{2}} + \frac{y ^{2}}{x ^{2}} - \frac{2 y}{x ^{2}} + \frac{1}{x ^{2}}

= \frac{x ^{2}}{x ^{2}} + \frac{y ^{2}}{x ^{2}} - \frac{2 y}{x ^{2}} + \frac{1}{x ^{2}}

Wende Regel an

\frac{a}{a} = 1

\frac{x ^{2}}{x ^{2}} = 1

= 1 + \frac{y ^{2}}{x ^{2}} - \frac{2 y}{x ^{2}} + \frac{1}{x ^{2}}

e x p an d \frac{2500 s ( 20 s + 200 )}{( s + 1 ) ( s ^{2} + 100 s + 10000 )}

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

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

e x p an d - \frac{2 s ( - s ^{2} - 27 )}{( s ^{2} - 9 ) ^{3}}

e x p an d 2 (\frac{x ^{2}}{2} + t^{2} + t = c)