erweitern ((x+y-1)^2)/(4x^2)

Lösung

erweitern

\frac{( x + y - 1 ) ^{2}}{4 x ^{2}}

\frac{y}{2 x} + \frac{1}{4} - \frac{1}{2 x} + \frac{y ^{2}}{4 x ^{2}} - \frac{y}{2 x ^{2}} + \frac{1}{4 x ^{2}}

Schritte zur Lösung

\frac{( x + y - 1 ) ^{2}}{4 x ^{2}}

(x + y - 1)^{2} = 2 x y + x^{2} - 2 x + y^{2} - 2 y + 1

= \frac{2 x y + x ^{2} - 2 x + y ^{2} - 2 y + 1}{4 x ^{2}}

Wende Bruchregel an:

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

\frac{2 x y + x ^{2} - 2 x + y ^{2} - 2 y + 1}{4 x ^{2}} = \frac{2 x y}{4 x ^{2}} + \frac{x ^{2}}{4 x ^{2}} - \frac{2 x}{4 x ^{2}} + \frac{y ^{2}}{4 x ^{2}} - \frac{2 y}{4 x ^{2}} + \frac{1}{4 x ^{2}}

= \frac{2 x y}{4 x ^{2}} + \frac{x ^{2}}{4 x ^{2}} - \frac{2 x}{4 x ^{2}} + \frac{y ^{2}}{4 x ^{2}} - \frac{2 y}{4 x ^{2}} + \frac{1}{4 x ^{2}}

\frac{2 x y}{4 x ^{2}} = \frac{y}{2 x}

\frac{x ^{2}}{4 x ^{2}} = \frac{1}{4}

\frac{2 x}{4 x ^{2}} = \frac{1}{2 x}

\frac{2 y}{4 x ^{2}} = \frac{y}{2 x ^{2}}

= \frac{y}{2 x} + \frac{1}{4} - \frac{1}{2 x} + \frac{y ^{2}}{4 x ^{2}} - \frac{y}{2 x ^{2}} + \frac{1}{4 x ^{2}}

e x p an d 3 x^{2} (x^{2} + sin (4 x))

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

s im pl i f y (cos (x) + i sin (x))^{7}

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

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