erweitern-(sinh(x)(x^2+1))/(2x)

Lösung

erweitern

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

- \frac{x sinh ( x )}{2} - \frac{sinh ( x )}{2 x}

Schritte zur Lösung

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

Multipliziere aus

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

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

Wende Bruchregel an:

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

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

= - (\frac{x ^{2} sinh ( x )}{2 x}) - (\frac{sinh ( x )}{2 x})

Entferne die Klammern:

(a) = a

= - \frac{x ^{2} sinh ( x )}{2 x} - \frac{sinh ( x )}{2 x}

Streiche

\frac{x ^{2} sinh ( x )}{2 x} : \frac{x sinh ( x )}{2}

= - \frac{x sinh ( x )}{2} - \frac{sinh ( x )}{2 x}

e x p an d (4 x^{2} - x y + y^{2}) d x + x^{2} d y

e x p an d π (1 - \frac{1}{e})

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

e x p an d \frac{3 x ^{2} + 4 x - 7}{( x + 1 ) ( x - 3 )}

e x p an d \frac{2 s + 5}{( s - 3 ) ^{2}}