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Partial Fractions

Improper Fractions

Convert $\frac{ 4x^4 + 12 x^2 + 8 x + 3 }{ x^3 + x }$ into partial fractions.

\frac{8 x + 5}{x+1} + \frac{5}{x} + 4 x + 4

\frac{5x + 8}{x^2+1} + \frac{3}{x} + 4

\frac{5x + 8}{x^2+1} + \frac{3}{x} + 4 x

\frac{5x + 5}{x^2+1} + \frac{8}{x} + 4 x + 3

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by Brilliant Staff

Convert $\frac{ 2x^4 +2 x^3 +2 x^2 +7 x -5 } { x^2-x }$ into partial fractions.

\frac{5}{x} + \frac{8}{x-1} + 2 x^2 - 6 x + 4

\frac{5}{x} + \frac{8}{x-1} + 2 x^2 + 4 x + 6

\frac{5}{x} - \frac{1}{x-1} + 2 x^2 + 4 x + 6

\frac{5}{x} + \frac{8}{x-1} + \frac{4}{x(x-1)} + 2 x^2 + 4 x + 6

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by Brilliant Staff

Convert $\frac{ 2 x^3 - 12 x^2 + 20x -3 } { x^2 - 6x + 9 }$ into partial fractions.

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

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

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

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

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Convert $\frac{ 3 x^3 -17 x^2 +32x -28 } { x^3 - 8x^2 + 20 x - 16 }$ into partial fractions.

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

\frac{2}{x-2} + \frac{4}{\left( x- 4 \right)^2} - \frac{5}{x -4} - 5

\frac{2}{x+2} + \frac{4}{\left( x+ 2 \right)^2} + \frac{5}{x +4} + 3

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

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by Brilliant Staff

Convert $\frac{ 4 x^5 + 34 x^4 + 60 x^3 + 256 x^2 + 183 x + 529 }{ x^5 + 7x^4 + 8 x^3 + 56 x^2 + 16 x + 112 }$ into partial fractions.

\frac{7 x}{x^2+ 4} + \frac{ 4 }{ \left( x^2+ 4 \right) ^2 } + \frac{4}{( x+7 )^2} + 2

\frac{4 x}{x^2+ 4} + \frac{ 7 }{ \left( x^2+ 4 \right) ^2 } + \frac{2}{x+7} + 4

\frac{4 x}{x^2+ 7} + \frac{ 7 }{ \left( x^2+ 7 \right) ^2 } + \frac{2}{x+4} + 4

\frac{7}{x^2+ 4} + \frac{ 4 x }{ \left( x^2+ 4 \right) ^2 } + \frac{2}{x+7} + 4

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by Brilliant Staff