erweitern (5(x^2+4))/((x^2-49)^9)

Lösung

erweitern

\frac{5 ( x ^{2} + 4 )}{( x ^{2} - 49 ) ^{9}}

\frac{5 x ^{2} + 20}{x ^{18} - 441 x ^{16} + 86436 x ^{14} - 9882516 x ^{12} + 726364926 x ^{10} - 35591881374 x ^{8} + 4 9 ^{6} \cdot 84 x ^{6} - 4 9 ^{7} \cdot 36 x ^{4} + 4 9 ^{8} \cdot 9 x ^{2} - 4 9 ^{9}}

Schritte zur Lösung

\frac{5 ( x ^{2} + 4 )}{( x ^{2} - 49 ) ^{9}}

(x^{2} - 49)^{9} = x^{18} - 441 x^{16} + 86436 x^{14} - 9882516 x^{12} + 726364926 x^{10} - 35591881374 x^{8} + 4 9^{6} \cdot 84 x^{6} - 4 9^{7} \cdot 36 x^{4} + 4 9^{8} \cdot 9 x^{2} - 4 9^{9}

= \frac{5 ( x ^{2} + 4 )}{x ^{18} - 441 x ^{16} + 86436 x ^{14} - 9882516 x ^{12} + 726364926 x ^{10} - 35591881374 x ^{8} + 4 9 ^{6} \cdot 84 x ^{6} - 4 9 ^{7} \cdot 36 x ^{4} + 4 9 ^{8} \cdot 9 x ^{2} - 4 9 ^{9}}

Multipliziere aus

5 (x^{2} + 4) : 5 x^{2} + 20

= \frac{5 x ^{2} + 20}{x ^{18} - 441 x ^{16} + 86436 x ^{14} - 9882516 x ^{12} + 726364926 x ^{10} - 35591881374 x ^{8} + 4 9 ^{6} \cdot 84 x ^{6} - 4 9 ^{7} \cdot 36 x ^{4} + 4 9 ^{8} \cdot 9 x ^{2} - 4 9 ^{9}}

s im pl i f y (t - i t^{2})^{2}

e x p an d 5 (15 + 22 e^{\frac{4 l n ( \frac{15}{22} )}{3}})

e x p an d (y^{4} + 8 x y^{4} - x^{3}) d x + (4 x y^{3} + 16 x^{2} y^{3}) d y

s im pl i f y (y - \frac{1}{3}) (y - \frac{2}{3})

e x p an d \frac{5 ( 3 x ^{3} + 2 x ) ^{\frac{3}{2}} ( 9 x ^{2} + 2 )}{2}