vereinfachen (1/(x^2)+1/(y^2))/(1/x-1/y)

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

Füge zusammen:

\frac{1}{x ^{2}} + \frac{1}{y ^{2}} : \frac{y ^{2} + x ^{2}}{x ^{2} y ^{2}}

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

Füge zusammen:

\frac{1}{x} - \frac{1}{y} : \frac{y - x}{x y}

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

Wende Bruchregel an:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

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

Streiche

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

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

0 = - \frac{2}{3} x - 2

f a c t or 6 x^{2} - 19 x + 15

s im pl i f y x^{- 2} \cdot x^{\frac{11}{9}}

\frac{2 ^{x} - 4}{lo g _{2} ( x )} > 0

k^{2} - 4 k + 5 = 0