erweitern ({(x-2)(x+2)(x-3)^6})/((x+3)^7)

Lösung

erweitern

\frac{{ ( x - 2 ) ( x + 2 ) ( x - 3 ) ^{6} }}{( x + 3 ) ^{7}}

\frac{x ^{8} - 18 x ^{7} + 131 x ^{6} - 468 x ^{5} + 675 x ^{4} + 702 x ^{3} - 4131 x ^{2} + 5832 x - 2916}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187}

Schritte zur Lösung

\frac{( x - 2 ) ( x + 2 ) ( x - 3 ) ^{6}}{( x + 3 ) ^{7}}

(x + 3)^{7} = x^{7} + 21 x^{6} + 189 x^{5} + 945 x^{4} + 2835 x^{3} + 5103 x^{2} + 5103 x + 2187

= \frac{( x - 2 ) ( x + 2 ) ( x - 3 ) ^{6}}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187}

(x - 3)^{6} = x^{6} - 18 x^{5} + 135 x^{4} - 540 x^{3} + 1215 x^{2} - 1458 x + 729

= \frac{( x - 2 ) ( x + 2 ) ( x ^{6} - 18 x ^{5} + 135 x ^{4} - 540 x ^{3} + 1215 x ^{2} - 1458 x + 729 )}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187}

Multipliziere aus

(x - 2) (x + 2) (x^{6} - 18 x^{5} + 135 x^{4} - 540 x^{3} + 1215 x^{2} - 1458 x + 729) : x^{8} - 18 x^{7} + 131 x^{6} - 468 x^{5} + 675 x^{4} + 702 x^{3} - 4131 x^{2} + 5832 x - 2916

= \frac{x ^{8} - 18 x ^{7} + 131 x ^{6} - 468 x ^{5} + 675 x ^{4} + 702 x ^{3} - 4131 x ^{2} + 5832 x - 2916}{x ^{7} + 21 x ^{6} + 189 x ^{5} + 945 x ^{4} + 2835 x ^{3} + 5103 x ^{2} + 5103 x + 2187}

e x p an d A (- 3, 1, - 2, 7) B (- 1, - 4)

e x p an d \frac{20 e ^{- 4 s} - 20 e ^{- 6 s}}{s ( s ^{2} + 4 s + 20 )}

e x p an d \frac{( x + i ) ^{9}}{( x - i ) ^{7}}

s im pl i f y (b - c d) (b + c d)

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