erweitern (2x+2h)/(sqrt(x^2+2xh+h^2+1))-(2x)/(sqrt(x^2+1))

Lösung

erweitern

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

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

Schritte zur Lösung

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

\frac{2 x + 2 h}{x ^{2} + 2 x h + h ^{2} + 1} = \frac{( 2 x + 2 h ) x ^{2} + 2 x h + h ^{2} + 1}{x ^{2} + 2 x h + h ^{2} + 1}

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

= \frac{( 2 x + 2 h ) x ^{2} + 2 x h + h ^{2} + 1}{x ^{2} + 2 x h + h ^{2} + 1} - \frac{2 x x ^{2} + 1}{x ^{2} + 1}

Multipliziere aus

(2 x + 2 h) x^{2} + 2 x h + h^{2} + 1 : 2 x x^{2} + 2 x h + h^{2} + 1 + 2 h x^{2} + 2 x h + h^{2} + 1

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

e x p an d ((3 6^{2} - y^{2}) - 13.5)^{2}

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

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

e x p an d \frac{( x + 1 ) ^{4}}{4}

e x p an d lo g_{2} (4 w z)