erweitern (3-5(x+h)^2-sqrt(3-5x^2))/(4h)

Lösung

erweitern

\frac{3 - 5 ( x + h ) ^{2} - 3 - 5 x ^{2}}{4 h}

\frac{3}{4 h} - \frac{5 x ^{2}}{4 h} - \frac{5 x}{2} - \frac{5 h}{4} - \frac{3 - 5 x ^{2}}{4 h}

Schritte zur Lösung

\frac{3 - 5 ( x + h ) ^{2} - 3 - 5 x ^{2}}{4 h}

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

= \frac{3 - 5 ( x ^{2} + 2 x h + h ^{2} ) - - 5 x ^{2} + 3}{4 h}

Multipliziere aus

3 - 5 (x^{2} + 2 x h + h^{2}) - 3 - 5 x^{2} : 3 - 5 x^{2} - 10 x h - 5 h^{2} - 3 - 5 x^{2}

= \frac{3 - 5 x ^{2} - 10 x h - 5 h ^{2} - - 5 x ^{2} + 3}{4 h}

Wende Bruchregel an:

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

\frac{3 - 5 x ^{2} - 10 x h - 5 h ^{2} - 3 - 5 x ^{2}}{4 h} = \frac{3}{4 h} - \frac{5 x ^{2}}{4 h} - \frac{10 x h}{4 h} - \frac{5 h ^{2}}{4 h} - \frac{3 - 5 x ^{2}}{4 h}

= \frac{3}{4 h} - \frac{5 x ^{2}}{4 h} - \frac{10 x h}{4 h} - \frac{5 h ^{2}}{4 h} - \frac{- 5 x ^{2} + 3}{4 h}

Streiche

\frac{10 x h}{4 h} : \frac{5 x}{2}

= \frac{3}{4 h} - \frac{5 x ^{2}}{4 h} - \frac{5 x}{2} - \frac{5 h ^{2}}{4 h} - \frac{- 5 x ^{2} + 3}{4 h}

Streiche

\frac{5 h ^{2}}{4 h} : \frac{5 h}{4}

= \frac{3}{4 h} - \frac{5 x ^{2}}{4 h} - \frac{5 x}{2} - \frac{5 h}{4} - \frac{- 5 x ^{2} + 3}{4 h}

e x p an d \frac{2 z ( z ^{2} + 2 z - 8 )}{( z - 1 ) ( z + 2 )}

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

e x p an d (8 x^{2} + 4 y) x^{2} + y^{2} = 1

e x p an d \frac{h ( α - ρ )}{α}

e x p an d 3 w^{2} (2 w^{2})