erweitern ((x^2+3x-5)z^2(z-3)^2+3)/(x^2+3x+4)

Lösung

erweitern

\frac{( x ^{2} + 3 x - 5 ) z ^{2} ( z - 3 ) ^{2} + 3}{x ^{2} + 3 x + 4}

\frac{x ^{2} z ^{4} - 6 x ^{2} z ^{3} + 9 x ^{2} z ^{2} + 3 x z ^{4} - 18 x z ^{3} + 27 x z ^{2} - 5 z ^{4} + 30 z ^{3} - 45 z ^{2} + 3}{x ^{2} + 3 x + 4}

Schritte zur Lösung

\frac{( x ^{2} + 3 x - 5 ) z ^{2} ( z - 3 ) ^{2} + 3}{x ^{2} + 3 x + 4}

(z - 3)^{2} = z^{2} - 6 z + 9

= \frac{z ^{2} ( x ^{2} + 3 x - 5 ) ( z ^{2} - 6 z + 9 ) + 3}{x ^{2} + 3 x + 4}

Multipliziere aus

(x^{2} + 3 x - 5) z^{2} (z^{2} - 6 z + 9) + 3 : x^{2} z^{4} - 6 x^{2} z^{3} + 9 x^{2} z^{2} + 3 x z^{4} - 18 x z^{3} + 27 x z^{2} - 5 z^{4} + 30 z^{3} - 45 z^{2} + 3

= \frac{x ^{2} z ^{4} - 6 x ^{2} z ^{3} + 9 x ^{2} z ^{2} + 3 x z ^{4} - 18 x z ^{3} + 27 x z ^{2} - 5 z ^{4} + 30 z ^{3} - 45 z ^{2} + 3}{x ^{2} + 3 x + 4}

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

s im pl i f y e^{t (- \frac{1}{a} + i)}

e x p an d \frac{- 6 x + 17}{( x + 3 ) ( 2 x - 1 )}

e x p an d - \frac{x ^{4} - 10 x ^{3} - 13 x ^{2} + 60 x + 36}{( x ^{2} - 5 x + 6 ) ^{2}}

e x p an d \frac{s + 1}{s ( s ^{2} - 7 s )}