longdivision ((11x^2*(33x^3)))/((4x+12x^2))

Lösung

schriftliche division

\frac{( 11 x ^{2} \cdot ( 33 x ^{3} ) )}{( 4 x + 12 x ^{2} )}

\frac{121 x ^{3}}{4} - \frac{121 x ^{2}}{12} + \frac{121 x}{36} - \frac{121}{108} + \frac{121}{108 ( 3 x + 1 )}

Schritte zur Lösung

\frac{( 11 x ^{2} ( 33 x ^{3} ) )}{( 4 x + 12 x ^{2} )}

Multipliziere aus

11 x^{2} \cdot 33 x^{3} : 363 x^{5}

= \frac{363 x ^{5}}{4 x + 12 x ^{2}}

Dividiere

\frac{363 x ^{5}}{12 x ^{2} + 4 x} : \frac{363 x ^{5}}{12 x ^{2} + 4 x} = \frac{121 x ^{3}}{4} + \frac{- 121 x ^{4}}{12 x ^{2} + 4 x}

= \frac{121 x ^{3}}{4} + \frac{- 121 x ^{4}}{12 x ^{2} + 4 x}

Dividiere

\frac{- 121 x ^{4}}{12 x ^{2} + 4 x} : \frac{- 121 x ^{4}}{12 x ^{2} + 4 x} = - \frac{121 x ^{2}}{12} + \frac{\frac{121 x ^{3}}{3}}{12 x ^{2} + 4 x}

= \frac{121 x ^{3}}{4} - \frac{121 x ^{2}}{12} + \frac{\frac{121 x ^{3}}{3}}{12 x ^{2} + 4 x}

Dividiere

\frac{\frac{121 x ^{3}}{3}}{12 x ^{2} + 4 x} : \frac{\frac{121 x ^{3}}{3}}{12 x ^{2} + 4 x} = \frac{121 x}{36} + \frac{- \frac{121 x ^{2}}{9}}{12 x ^{2} + 4 x}

= \frac{121 x ^{3}}{4} - \frac{121 x ^{2}}{12} + \frac{121 x}{36} + \frac{- \frac{121 x ^{2}}{9}}{12 x ^{2} + 4 x}

Dividiere

\frac{- \frac{121 x ^{2}}{9}}{12 x ^{2} + 4 x} : \frac{- \frac{121 x ^{2}}{9}}{12 x ^{2} + 4 x} = - \frac{121}{108} + \frac{\frac{121 x}{27}}{12 x ^{2} + 4 x}

= \frac{121 x ^{3}}{4} - \frac{121 x ^{2}}{12} + \frac{121 x}{36} - \frac{121}{108} + \frac{\frac{121 x}{27}}{12 x ^{2} + 4 x}

Vereinfache

= \frac{121 x ^{3}}{4} - \frac{121 x ^{2}}{12} + \frac{121 x}{36} - \frac{121}{108} + \frac{121}{108 ( 3 x + 1 )}

s im pl i f y \frac{92}{100}

q u a d r a t i c f or m u l a x^{2} - 8 x - 16 = 0

s im pl i f y 3.2%

so l v e f or x, 2 x - 1 = 7

s im pl i f y 2 x \cdot (3 x)