erweitern ((2+x)(3+2x)^2)/((1.8-2x)^2(1-2x)^2)

Lösung

erweitern

\frac{( 2 + x ) ( 3 + 2 x ) ^{2}}{( 1.8 - 2 x ) ^{2} ( 1 - 2 x ) ^{2}}

\frac{4 x ^{3} + 20 x ^{2} + 33 x + 18}{16 x ^{4} - 44.8 x ^{3} + 45.76 x ^{2} - 20.16 x + 3.24}

Schritte zur Lösung

\frac{( 2 + x ) ( 3 + 2 x ) ^{2}}{( 1.8 - 2 x ) ^{2} ( 1 - 2 x ) ^{2}}

(1.8 - 2 x)^{2} = 3.24 - 7.2 x + 4 x^{2}

= \frac{( x + 2 ) ( 2 x + 3 ) ^{2}}{( 4 x ^{2} - 7.2 x + 3.24 ) ( - 2 x + 1 ) ^{2}}

(1 - 2 x)^{2} = 1 - 4 x + 4 x^{2}

= \frac{( x + 2 ) ( 2 x + 3 ) ^{2}}{( 4 x ^{2} - 7.2 x + 3.24 ) ( 4 x ^{2} - 4 x + 1 )}

(3 + 2 x)^{2} = 9 + 12 x + 4 x^{2}

= \frac{( x + 2 ) ( 4 x ^{2} + 12 x + 9 )}{( 4 x ^{2} - 7.2 x + 3.24 ) ( 4 x ^{2} - 4 x + 1 )}

Multipliziere aus

(3.24 - 7.2 x + 4 x^{2}) (1 - 4 x + 4 x^{2}) : 16 x^{4} - 44.8 x^{3} + 45.76 x^{2} - 20.16 x + 3.24

= \frac{( x + 2 ) ( 4 x ^{2} + 12 x + 9 )}{16 x ^{4} - 44.8 x ^{3} + 45.76 x ^{2} - 20.16 x + 3.24}

Multipliziere aus

(2 + x) (9 + 12 x + 4 x^{2}) : 4 x^{3} + 20 x^{2} + 33 x + 18

= \frac{4 x ^{3} + 20 x ^{2} + 33 x + 18}{16 x ^{4} - 44.8 x ^{3} + 45.76 x ^{2} - 20.16 x + 3.24}

e x p an d x (4 - x + 2)

e x p an d \frac{( k ( k + 1 ) ( k + 2 ) )}{3}

e x p an d \frac{s - 1}{( s - 2 ) ( s - 3 )}

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

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