erweitern ((x+7)(x-3))/(x^2)

Lösung

erweitern

\frac{( x + 7 ) ( x - 3 )}{x ^{2}}

1 + \frac{4}{x} - \frac{21}{x ^{2}}

Schritte zur Lösung

\frac{( x + 7 ) ( x - 3 )}{x ^{2}}

Multipliziere aus

(x + 7) (x - 3) : x^{2} + 4 x - 21

= \frac{x ^{2} + 4 x - 21}{x ^{2}}

Wende Bruchregel an:

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

\frac{x ^{2} + 4 x - 21}{x ^{2}} = \frac{x ^{2}}{x ^{2}} + \frac{4 x}{x ^{2}} - \frac{21}{x ^{2}}

= \frac{x ^{2}}{x ^{2}} + \frac{4 x}{x ^{2}} - \frac{21}{x ^{2}}

Wende Regel an

\frac{a}{a} = 1

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

= 1 + \frac{4 x}{x ^{2}} - \frac{21}{x ^{2}}

Streiche

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

= 1 + \frac{4}{x} - \frac{21}{x ^{2}}

e x p an d (y + \frac{5}{6})^{2}

e x p an d \frac{1}{( T s + 1 ) ( s ^{2} )}

s im pl i f y 7 (x - \frac{1}{2})

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

e x p an d \frac{x}{( x ^{2} + k ) ( x ^{2} + b x + c )}