erweitern (6(44x^3+72x^2-36x-63))/((4x^2+9x+6)^3)

Lösung

erweitern

\frac{6 ( 44 x ^{3} + 72 x ^{2} - 36 x - 63 )}{( 4 x ^{2} + 9 x + 6 ) ^{3}}

\frac{264 x ^{3} + 432 x ^{2} - 216 x - 378}{64 x ^{6} + 432 x ^{5} + 1260 x ^{4} + 2025 x ^{3} + 1890 x ^{2} + 972 x + 216}

Schritte zur Lösung

\frac{6 ( 44 x ^{3} + 72 x ^{2} - 36 x - 63 )}{( 4 x ^{2} + 9 x + 6 ) ^{3}}

(4 x^{2} + 9 x + 6)^{3} = 64 x^{6} + 432 x^{5} + 1260 x^{4} + 2025 x^{3} + 1890 x^{2} + 972 x + 216

= \frac{6 ( 44 x ^{3} + 72 x ^{2} - 36 x - 63 )}{64 x ^{6} + 432 x ^{5} + 1260 x ^{4} + 2025 x ^{3} + 1890 x ^{2} + 972 x + 216}

Multipliziere aus

6 (44 x^{3} + 72 x^{2} - 36 x - 63) : 264 x^{3} + 432 x^{2} - 216 x - 378

= \frac{264 x ^{3} + 432 x ^{2} - 216 x - 378}{64 x ^{6} + 432 x ^{5} + 1260 x ^{4} + 2025 x ^{3} + 1890 x ^{2} + 972 x + 216}

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

s im pl i f y (e^{- i 2 t} - e^{- i 3 t}) (e^{+ i 2 t} - e^{+ i 3 t})

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

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

e x p an d \frac{2 x + 6}{( s - 1 ) ^{3}}