What is longdivision ((x^3+2x^2))/((3x^2-1)) ?

The solution to longdivision ((x^3+2x^2))/((3x^2-1)) is x/3+2/3+(x+2)/(3(3x^2-1))

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longdivision ((x^3+2x^2))/((3x^2-1))

long division

\frac{( x ^{3} + 2 x ^{2} )}{( 3 x ^{2} - 1 )}

\frac{x}{3} + \frac{2}{3} + \frac{x + 2}{3 ( 3 x ^{2} - 1 )}

Solution steps

\frac{( x ^{3} + 2 x ^{2} )}{( 3 x ^{2} - 1 )}

Divide

\frac{x ^{3} + 2 x ^{2}}{3 x ^{2} - 1} : \frac{x ^{3} + 2 x ^{2}}{3 x ^{2} - 1} = \frac{x}{3} + \frac{2 x ^{2} + \frac{x}{3}}{3 x ^{2} - 1}

= \frac{x}{3} + \frac{2 x ^{2} + \frac{x}{3}}{3 x ^{2} - 1}

Divide

\frac{2 x ^{2} + \frac{x}{3}}{3 x ^{2} - 1} : \frac{2 x ^{2} + \frac{x}{3}}{3 x ^{2} - 1} = \frac{2}{3} + \frac{\frac{x}{3} + \frac{2}{3}}{3 x ^{2} - 1}

= \frac{x}{3} + \frac{2}{3} + \frac{\frac{x}{3} + \frac{2}{3}}{3 x ^{2} - 1}

Simplify

= \frac{x}{3} + \frac{2}{3} + \frac{x + 2}{3 ( 3 x ^{2} - 1 )}

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

\frac{( n + 2 )}{( n + 1 )}

\frac{( a + 2 )}{( a - 2 )}

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

\frac{( 2 x + 3 )}{( x + 1 )}

What is longdivision ((x^3+2x^2))/((3x^2-1)) ?
The solution to longdivision ((x^3+2x^2))/((3x^2-1)) is x/3+2/3+(x+2)/(3(3x^2-1))