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

Lösung

erweitern

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

\frac{8}{3 x ^{\frac{1}{3}} ( 4 - x ) ^{\frac{5}{3}}} - (\frac{x ^{2}}{1024 - 1280 x + 640 x ^{2} - 160 x ^{3} + 20 x ^{4} - x ^{5}})^{\frac{1}{3}}

Schritte zur Lösung

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

Wende Bruchregel an:

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

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

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

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

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

\frac{x ^{2}}{( 4 - x ) ^{5}} = \frac{x ^{2}}{1024 - 1280 x + 640 x ^{2} - 160 x ^{3} + 20 x ^{4} - x ^{5}}

= \frac{8}{3 x ^{\frac{1}{3}} ( - x + 4 ) ^{\frac{5}{3}}} - (\frac{x ^{2}}{- x ^{5} + 20 x ^{4} - 160 x ^{3} + 640 x ^{2} - 1280 x + 1024})^{\frac{1}{3}}

e x p an d \frac{x ^{2}}{( 0.860708 - 1.8560668 x + x ^{2} ) \cdot ( x - 1 )}

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

s im pl i f y 128 (sin^{2} (t) + 128 cos^{2} (t))

e x p an d cot (θ) (sin (θ) + sec (θ))

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