erweitern (ax+y+sqrt((ax+y)^2+z^2))/z

Lösung

erweitern

\frac{a x + y + ( a x + y ) ^{2} + z ^{2}}{z}

\frac{a x}{z} + \frac{y}{z} + \frac{a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

Schritte zur Lösung

\frac{a x + y + ( a x + y ) ^{2} + z ^{2}}{z}

Multipliziere aus

(a x + y)^{2} + z^{2} : a^{2} x^{2} + 2 a x y + y^{2} + z^{2}

= \frac{a x + y + a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

Wende Bruchregel an:

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

\frac{a x + y + a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z} = \frac{a x}{z} + \frac{y}{z} + \frac{a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

= \frac{a x}{z} + \frac{y}{z} + \frac{a ^{2} x ^{2} + 2 a x y + y ^{2} + z ^{2}}{z}

e x p an d, (3 - 9) (3 - 5)

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

e x p an d (e^{x} + e^{x} x) \cdot e^{x}

e x p an d \frac{2}{s ( s ^{2} + 7 s + 12 )} + \frac{e ^{- 2 s}}{s ^{2} + 7 s + 12}

e x p an d (x + i) (3 - y)