erweitern ((x^2+3)^{2/3}(3x+2)^2)/(sqrt(x+1))

Lösung

erweitern

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

\frac{9 x ^{2} ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1} + \frac{12 x ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1} + \frac{4 ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1}

Schritte zur Lösung

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

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

= \frac{( 9 x ^{2} + 12 x + 4 ) ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1}

Multipliziere aus

(x^{2} + 3)^{\frac{2}{3}} (9 x^{2} + 12 x + 4) : 9 x^{2} (x^{2} + 3)^{\frac{2}{3}} + 12 x (x^{2} + 3)^{\frac{2}{3}} + 4 (x^{2} + 3)^{\frac{2}{3}}

= \frac{9 x ^{2} ( x ^{2} + 3 ) ^{\frac{2}{3}} + 12 x ( x ^{2} + 3 ) ^{\frac{2}{3}} + 4 ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1}

Wende Bruchregel an:

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

\frac{9 x ^{2} ( x ^{2} + 3 ) ^{\frac{2}{3}} + 12 x ( x ^{2} + 3 ) ^{\frac{2}{3}} + 4 ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1} = \frac{9 x ^{2} ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1} + \frac{12 x ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1} + \frac{4 ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1}

= \frac{9 x ^{2} ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1} + \frac{12 x ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1} + \frac{4 ( x ^{2} + 3 ) ^{\frac{2}{3}}}{x + 1}

\frac{d}{d v} ((p) (p + \frac{1.3}{v ^{2}}) (v - 9))

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

s im pl i f y (cos (x)) (2 + cos (x))

e x p an d \frac{18 x}{( 9 - x ^{2} ) ^{2}}

e x p an d \frac{( sin ( a ) + tan ( a ) ) cot ( a )}{csc ( a ) + cot ( a )}