longdivision ((5x^3-14-20x+x^4))/((x^2-x-3))

Lösung

schriftliche division

\frac{( 5 x ^{3} - 14 - 20 x + x ^{4} )}{( x ^{2} - x - 3 )}

x^{2} + 6 x + 9 + \frac{7 x + 13}{x ^{2} - x - 3}

Schritte zur Lösung

\frac{( 5 x ^{3} - 14 - 20 x + x ^{4} )}{( x ^{2} - x - 3 )}

Dividiere

\frac{x ^{4} + 5 x ^{3} - 20 x - 14}{x ^{2} - x - 3} : \frac{x ^{4} + 5 x ^{3} - 20 x - 14}{x ^{2} - x - 3} = x^{2} + \frac{6 x ^{3} + 3 x ^{2} - 20 x - 14}{x ^{2} - x - 3}

= x^{2} + \frac{6 x ^{3} + 3 x ^{2} - 20 x - 14}{x ^{2} - x - 3}

Dividiere

\frac{6 x ^{3} + 3 x ^{2} - 20 x - 14}{x ^{2} - x - 3} : \frac{6 x ^{3} + 3 x ^{2} - 20 x - 14}{x ^{2} - x - 3} = 6 x + \frac{9 x ^{2} - 2 x - 14}{x ^{2} - x - 3}

= x^{2} + 6 x + \frac{9 x ^{2} - 2 x - 14}{x ^{2} - x - 3}

Dividiere

\frac{9 x ^{2} - 2 x - 14}{x ^{2} - x - 3} : \frac{9 x ^{2} - 2 x - 14}{x ^{2} - x - 3} = 9 + \frac{7 x + 13}{x ^{2} - x - 3}

= x^{2} + 6 x + 9 + \frac{7 x + 13}{x ^{2} - x - 3}

s im pl i f y \frac{144}{49}

so l v e f or x, 2 x^{2} - 5 x = 12

so l v e f or x, 6 < x + 5 \leq 11

so l v e f or b, 5 b = 27 + 8 (b - 3)

so l v e f or f, G f = h