erweitern (x^3+xy^2-y+y^3+x^2y+x=0)(1/(x^2y^2))

Lösung

erweitern

(x^{3} + x y^{2} - y + y^{3} + x^{2} y + x = 0) (\frac{1}{x ^{2} y ^{2}})

\frac{x}{y ^{2}} + \frac{1}{x} - \frac{1}{x ^{2} y} + \frac{y}{x ^{2}} + \frac{1}{y} + \frac{1}{x y ^{2}} = 0

Schritte zur Lösung

(x^{3} + x y^{2} - y + y^{3} + x^{2} y + x = 0) (\frac{1}{x ^{2} y ^{2}})

= (\frac{1}{x ^{2} y ^{2}}) (x^{3} + x y^{2} - y + y^{3} + x^{2} y + 0 = x)

Setze Klammern

(\frac{1}{x ^{2} y ^{2}}) x^{3} + (\frac{1}{x ^{2} y ^{2}}) x y^{2} + (\frac{1}{x ^{2} y ^{2}}) (- y) + (\frac{1}{x ^{2} y ^{2}}) y^{3} + (\frac{1}{x ^{2} y ^{2}}) x^{2} y + (\frac{1}{x ^{2} y ^{2}}) x = 0

Wende Minus-Plus Regeln an

+ (- a) = - a

(\frac{1}{x ^{2} y ^{2}}) x^{3} + (\frac{1}{x ^{2} y ^{2}}) x y^{2} - (\frac{1}{x ^{2} y ^{2}}) y + (\frac{1}{x ^{2} y ^{2}}) y^{3} + (\frac{1}{x ^{2} y ^{2}}) x^{2} y + (\frac{1}{x ^{2} y ^{2}}) x = 0

Multipliziere aus

(\frac{1}{x ^{2} y ^{2}}) x^{3} + (\frac{1}{x ^{2} y ^{2}}) x y^{2} - (\frac{1}{x ^{2} y ^{2}}) y + (\frac{1}{x ^{2} y ^{2}}) y^{3} + (\frac{1}{x ^{2} y ^{2}}) x^{2} y + (\frac{1}{x ^{2} y ^{2}}) x : \frac{x}{y ^{2}} + \frac{1}{x} - \frac{1}{x ^{2} y} + \frac{y}{x ^{2}} + \frac{1}{y} + \frac{1}{x y ^{2}}

\frac{x}{y ^{2}} + \frac{1}{x} - \frac{1}{x ^{2} y} + \frac{y}{x ^{2}} + \frac{1}{y} + \frac{1}{x y ^{2}} = 0

e x p an d \frac{x ^{5} + x}{( x + 1 ) ^{2} ( x - 2 )}

e x p an d 6 (x - 3 = x + 2 + x)

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

s im pl i f y (2 u + \frac{2}{3} v)^{2}

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