erweitern ((x+2)(x+5))/(x^2)

Lösung

erweitern

\frac{( x + 2 ) ( x + 5 )}{x ^{2}}

1 + \frac{7}{x} + \frac{10}{x ^{2}}

Schritte zur Lösung

\frac{( x + 2 ) ( x + 5 )}{x ^{2}}

Multipliziere aus

(x + 2) (x + 5) : x^{2} + 7 x + 10

= \frac{x ^{2} + 7 x + 10}{x ^{2}}

Wende Bruchregel an:

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

\frac{x ^{2} + 7 x + 10}{x ^{2}} = \frac{x ^{2}}{x ^{2}} + \frac{7 x}{x ^{2}} + \frac{10}{x ^{2}}

= \frac{x ^{2}}{x ^{2}} + \frac{7 x}{x ^{2}} + \frac{10}{x ^{2}}

Wende Regel an

\frac{a}{a} = 1

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

= 1 + \frac{7 x}{x ^{2}} + \frac{10}{x ^{2}}

Streiche

\frac{7 x}{x ^{2}} : \frac{7}{x}

= 1 + \frac{7}{x} + \frac{10}{x ^{2}}

e x p an d \frac{3 ( 4 s + 19 )}{( 2 s + 7 ) ( s + 4 )}

e x p an d x + Δ x (x + Δ x - 4)

e x p an d 11 x^{5 \cdot (2 m + 1)}

e x p an d \frac{( x ^{2} + 1 ) ^{2}}{x ^{4}}

e x p an d (\cdot + y) (3 + z)