erweitern (3(x^2+1)^{5/2}-5(x^2+1)^{3/2})/(15)

Lösung

erweitern

\frac{3 ( x ^{2} + 1 ) ^{\frac{5}{2}} - 5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15}

\frac{( x ^{2} + 1 ) ^{\frac{5}{2}}}{5} - \frac{( x ^{2} + 1 ) ^{\frac{3}{2}}}{3}

Schritte zur Lösung

\frac{3 ( x ^{2} + 1 ) ^{\frac{5}{2}} - 5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15}

Wende Bruchregel an:

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

\frac{3 ( x ^{2} + 1 ) ^{\frac{5}{2}} - 5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15} = \frac{3 ( x ^{2} + 1 ) ^{\frac{5}{2}}}{15} - \frac{5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15}

= \frac{3 ( x ^{2} + 1 ) ^{\frac{5}{2}}}{15} - \frac{5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15}

Streiche

\frac{3 ( x ^{2} + 1 ) ^{\frac{5}{2}}}{15} : \frac{( x ^{2} + 1 ) ^{\frac{5}{2}}}{5}

= \frac{( x ^{2} + 1 ) ^{\frac{5}{2}}}{5} - \frac{5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15}

Streiche

\frac{5 ( x ^{2} + 1 ) ^{\frac{3}{2}}}{15} : \frac{( x ^{2} + 1 ) ^{\frac{3}{2}}}{3}

= \frac{( x ^{2} + 1 ) ^{\frac{5}{2}}}{5} - \frac{( x ^{2} + 1 ) ^{\frac{3}{2}}}{3}

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

e x p an d \frac{2}{3} (a + 3) (b + (- \frac{4}{3}))

e x p an d \frac{1}{81} (2 + s)^{4}

e x p an d e^{(y + 1)^{2}} ((y^{2} + y) d x - x d y)

e x p an d (63 - 5) (25 + 42)