erweitern ((sqrt(16+x)-4)(x+2)(sqrt(9+x)+3))/x

Lösung

erweitern

\frac{( 16 + x - 4 ) ( x + 2 ) ( 9 + x + 3 )}{x}

144 + 25 x + x^{2} + 3 x + 16 + \frac{2 144 + 25 x + x ^{2}}{x} + \frac{6 16 + x}{x} - 4 x + 9 - 12 - \frac{8 9 + x}{x} - \frac{24}{x}

Schritte zur Lösung

\frac{( 16 + x - 4 ) ( x + 2 ) ( 9 + x + 3 )}{x}

Multipliziere aus

(16 + x - 4) (x + 2) (9 + x + 3) : x 144 + 25 x + x^{2} + 3 x 16 + x + 2 144 + 25 x + x^{2} + 6 16 + x - 4 x 9 + x - 12 x - 8 9 + x - 24

= \frac{x x ^{2} + 25 x + 144 + 3 x x + 16 + 2 x ^{2} + 25 x + 144 + 6 x + 16 - 4 x x + 9 - 12 x - 8 x + 9 - 24}{x}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x 144 + 25 x + x ^{2} + 3 x 16 + x + 2 144 + 25 x + x ^{2} + 6 16 + x - 4 x 9 + x - 12 x - 8 9 + x - 24}{x} = \frac{x 144 + 25 x + x ^{2}}{x} + \frac{3 x 16 + x}{x} + \frac{2 144 + 25 x + x ^{2}}{x} + \frac{6 16 + x}{x} - \frac{4 x 9 + x}{x} - \frac{12 x}{x} - \frac{8 9 + x}{x} - \frac{24}{x}

= \frac{x x ^{2} + 25 x + 144}{x} + \frac{3 x x + 16}{x} + \frac{2 x ^{2} + 25 x + 144}{x} + \frac{6 x + 16}{x} - \frac{4 x x + 9}{x} - \frac{12 x}{x} - \frac{8 x + 9}{x} - \frac{24}{x}

\frac{x 144 + 25 x + x ^{2}}{x} = 144 + 25 x + x^{2}

\frac{3 x 16 + x}{x} = 3 x + 16

\frac{4 x 9 + x}{x} = 4 x + 9

\frac{12 x}{x} = 12

= x^{2} + 25 x + 144 + 3 x + 16 + \frac{2 x ^{2} + 25 x + 144}{x} + \frac{6 x + 16}{x} - 4 x + 9 - 12 - \frac{8 x + 9}{x} - \frac{24}{x}

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

e x p an d (u y - y) d y

e x p an d \frac{( 20 + y ) y}{20 + 2 y}

e x p an d \frac{8 x ^{4} - 8 x ^{3} + 38 x ^{2} - 42 x + 28}{( x - 3 ) ( x ^{2} + 4 )}

e x p an d \frac{( 2 s ^{3} - s ^{2} )}{( 4 s ^{2} + 4 s + 5 ) ^{2}}