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Popular Algebra >

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

Solution

long division

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

Solution

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

Solution steps

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

Expand

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

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

Divide

\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}

Divide

\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}

Divide

\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}

Divide

\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}

Simplify

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

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