erweitern (8x-5)/(3(5x+8)^{4/3)(x^2+1)^{5/6}}

Lösung

erweitern

\frac{8 x - 5}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}}

\frac{8 x}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}} - \frac{5}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}}

Schritte zur Lösung

\frac{8 x - 5}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}}

Wende Bruchregel an:

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

\frac{8 x - 5}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}} = \frac{8 x}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}} - \frac{5}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}}

= \frac{8 x}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}} - \frac{5}{3 ( 5 x + 8 ) ^{\frac{4}{3}} ( x ^{2} + 1 ) ^{\frac{5}{6}}}

s im pl i f y (x - 4 x + 5) \cdot (x + 4 x + 5)

e x p an d (e^{x} + e^{- x}) \cdot (e^{x} - e^{- x})

e x p an d \frac{s ^{5} + 4 s ^{4} - s ^{3} + 2 s - 1}{( s - 4 ) ^{4} ( s ^{2} + 2 s + 3 )}

s im pl i f y e^{- i \cdot (\frac{π}{2} - x)}

e x p an d (1 - sin (θ))^{2} + (cos (θ))^{2}