erweitern ((x-3)(x^2+9)^3)/((2x-5)^2)

Lösung

erweitern

\frac{( x - 3 ) ( x ^{2} + 9 ) ^{3}}{( 2 x - 5 ) ^{2}}

\frac{x ^{7} + 27 x ^{5} + 243 x ^{3} + 729 x - 3 x ^{6} - 81 x ^{4} - 729 x ^{2} - 2187}{4 x ^{2} - 20 x + 25}

Schritte zur Lösung

\frac{( x - 3 ) ( x ^{2} + 9 ) ^{3}}{( 2 x - 5 ) ^{2}}

(2 x - 5)^{2} = 4 x^{2} - 20 x + 25

= \frac{( x - 3 ) ( x ^{2} + 9 ) ^{3}}{4 x ^{2} - 20 x + 25}

(x^{2} + 9)^{3} = x^{6} + 27 x^{4} + 243 x^{2} + 729

= \frac{( x - 3 ) ( x ^{6} + 27 x ^{4} + 243 x ^{2} + 729 )}{4 x ^{2} - 20 x + 25}

Multipliziere aus

(x - 3) (x^{6} + 27 x^{4} + 243 x^{2} + 729) : x^{7} + 27 x^{5} + 243 x^{3} + 729 x - 3 x^{6} - 81 x^{4} - 729 x^{2} - 2187

= \frac{x ^{7} + 27 x ^{5} + 243 x ^{3} + 729 x - 3 x ^{6} - 81 x ^{4} - 729 x ^{2} - 2187}{4 x ^{2} - 20 x + 25}

s im pl i f y (\frac{a - 1}{a} + \frac{1}{2}) x

s im pl i f y (a + 2)^{2}

e x p an d 5 (7 - 12)

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

e x p an d \frac{( 1 - 7 x )}{( ( 1 + x ) ( 1 - x ) )}