vereinfachen (sqrt(x/y)-sqrt(y/z))^2

Lösung

vereinfachen

(\frac{x}{y} - \frac{y}{z})^{2}

\frac{- 2 \frac{x}{y} \frac{y}{z} yz + x z + y ^{2}}{yz}

Schritte zur Lösung

(\frac{x}{y} - \frac{y}{z})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

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

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

Vereinfache

(\frac{x}{y})^{2} - 2 \frac{x}{y} \frac{y}{z} + (\frac{y}{z})^{2} : \frac{- 2 \frac{x}{y} \frac{y}{z} yz + x z + y ^{2}}{yz}

= \frac{- 2 \frac{x}{y} \frac{y}{z} yz + x z + y ^{2}}{yz}

e x p an d \frac{6 ( 7 ^{20} - 5 ^{20} )}{7 ^{20}} - \frac{144}{49}

e x p an d \frac{( x - 3 ) ( x + 3 )}{( x - 4 ) ( x + 4 )}

e x p an d (\frac{1}{3 x} - 2 x^{2})^{6}

s im pl i f y - \frac{28735}{( x - 42.8 ) ^{2}} + \frac{0.0000072}{x ^{3}}

e x p an d \frac{cos ^{2} ( x )}{( 1 - sin ( x ) ) ^{2}}