erweitern (sqrt(x+2)(3-x)^4)/((x+1)^5)

Lösung

erweitern

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

\frac{81 x + 2 - 108 x x + 2 + 54 x ^{2} x + 2 - 12 x ^{3} x + 2 + x ^{4} x + 2}{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 1}

Schritte zur Lösung

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

(x + 1)^{5} = x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 1

= \frac{( - x + 3 ) ^{4} x + 2}{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 1}

(3 - x)^{4} = 81 - 108 x + 54 x^{2} - 12 x^{3} + x^{4}

= \frac{( x ^{4} - 12 x ^{3} + 54 x ^{2} - 108 x + 81 ) x + 2}{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 1}

Multipliziere aus

x + 2 (81 - 108 x + 54 x^{2} - 12 x^{3} + x^{4}) : 81 x + 2 - 108 x x + 2 + 54 x^{2} x + 2 - 12 x^{3} x + 2 + x^{4} x + 2

= \frac{81 x + 2 - 108 x x + 2 + 54 x ^{2} x + 2 - 12 x ^{3} x + 2 + x ^{4} x + 2}{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 1}

e x p an d \frac{50}{( s + 2 ) ^{2}}

e x p an d \frac{6}{( x + 2 ) ^{3}}

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

e x p an d (cos (x) - sin (x)) \cdot cos (x)

s im pl i f y - i x (2 - i) (5 x + 6 i)