erweitern ((c+x)^2)/(c^2x^2)

Lösung

erweitern

\frac{( c + x ) ^{2}}{c ^{2} x ^{2}}

\frac{1}{x ^{2}} + \frac{2}{c x} + \frac{1}{c ^{2}}

Schritte zur Lösung

\frac{( c + x ) ^{2}}{c ^{2} x ^{2}}

(c + x)^{2} = c^{2} + 2 c x + x^{2}

= \frac{c ^{2} + 2 c x + x ^{2}}{c ^{2} x ^{2}}

Wende Bruchregel an:

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

\frac{c ^{2} + 2 c x + x ^{2}}{c ^{2} x ^{2}} = \frac{c ^{2}}{c ^{2} x ^{2}} + \frac{2 c x}{c ^{2} x ^{2}} + \frac{x ^{2}}{c ^{2} x ^{2}}

= \frac{c ^{2}}{c ^{2} x ^{2}} + \frac{2 c x}{c ^{2} x ^{2}} + \frac{x ^{2}}{c ^{2} x ^{2}}

Streiche

\frac{c ^{2}}{c ^{2} x ^{2}} : \frac{1}{x ^{2}}

= \frac{1}{x ^{2}} + \frac{2 c x}{c ^{2} x ^{2}} + \frac{x ^{2}}{c ^{2} x ^{2}}

Streiche

\frac{2 c x}{c ^{2} x ^{2}} : \frac{2}{c x}

= \frac{1}{x ^{2}} + \frac{2}{c x} + \frac{x ^{2}}{c ^{2} x ^{2}}

Streiche

\frac{x ^{2}}{c ^{2} x ^{2}} : \frac{1}{c ^{2}}

= \frac{1}{x ^{2}} + \frac{2}{c x} + \frac{1}{c ^{2}}

e x p an d (3 - 1) a l

e x p an d c u r l (y, - x, 0)

e x p an d 2 (x + 1) ln (x + 1)

e x p an d (1 + 2 i ∣)^{2}

e x p an d (- 4, - 5) y (1, 3)