erweitern (A(x^2+1)+(Bx+C)(x+3))/((x+3)(x^2+1))

Lösung

erweitern

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

\frac{A x ^{2} + A + B x ^{2} + 3 B x + C x + 3 C}{x ^{3} + x + 3 x ^{2} + 3}

Schritte zur Lösung

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

Multipliziere aus

(x + 3) (x^{2} + 1) : x^{3} + x + 3 x^{2} + 3

= \frac{A ( x ^{2} + 1 ) + ( B x + C ) ( x + 3 )}{x ^{3} + x + 3 x ^{2} + 3}

Multipliziere aus

A (x^{2} + 1) + (B x + C) (x + 3) : A x^{2} + A + B x^{2} + 3 B x + C x + 3 C

= \frac{A x ^{2} + A + B x ^{2} + 3 B x + C x + 3 C}{x ^{3} + x + 3 x ^{2} + 3}

e x p an d (1 + \frac{5}{x + 1}) \cdot (2 x + 5 ln ∣ x + 1 ∣)

e x p an d (1 + 8)^{\frac{1}{2}}

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

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

e x p an d 4 (sin (4) cos (4) + x cos (2 4^{\circ}))