erweitern (-y^2+(x-2)^2)/(y^3)

Lösung

erweitern

\frac{- y ^{2} + ( x - 2 ) ^{2}}{y ^{3}}

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

Schritte zur Lösung

\frac{- y ^{2} + ( x - 2 ) ^{2}}{y ^{3}}

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

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

Streiche

\frac{y ^{2}}{y ^{3}} : \frac{1}{y}

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

e x p an d \frac{1}{( y - m ) ( y - n )}

e x p an d - \frac{2 x ^{2} + 5 x + 9}{( x ^{2} + 7 ) ( x - 1 )}

e x p an d \frac{1}{( 6 x + 5 ) ^{9}}

e x p an d \frac{x ( x - 1 ) ( x - 2 )}{6}

e x p an d (e - 5) (f - 2 g)