Partial fractions with quadratic in denominator

3 Express \(\frac { 7 x ^ { 2 } - 3 x + 2 } { x \left( x ^ { 2 } + 1 \right) }\) in partial fractions.

5 Express \(\frac { 4 } { x \left( x ^ { 2 } + 4 \right) }\) in partial fractions.

2 Express \(\frac { 3 x } { ( 2 - x ) \left( 4 + x ^ { 2 } \right) } \quad\) in partial fractions.

4 Express \(\frac { 1 } { ( 2 x + 1 ) \left( x ^ { 2 } + 1 \right) }\) in partial fractions.

3 Express \(\frac { 3 x + 2 } { x \left( x ^ { 2 } + 1 \right) }\) in partial fractions.

4 Express \(\frac { 4 } { x \left( x ^ { 2 } + 4 \right) }\) in partial fractions.

1 It is given that \(\mathrm { f } ( x ) = \frac { 2 a x } { ( x - 2 a ) \left( x ^ { 2 } + a ^ { 2 } \right) }\), where \(a\) is a non-zero constant. Express \(\mathrm { f } ( x )\) in partial fractions.

1 Express \(\frac { 2 x + 3 } { ( x + 3 ) \left( x ^ { 2 } + 9 \right) }\) in partial fractions.

1 Express \(\frac { 3 x + 2 } { x \left( x ^ { 2 } + 1 \right) }\) in partial fractions.

1 Express \(\frac { 1 } { ( 2 x + 1 ) \left( x ^ { 2 } + 1 \right) }\) in partial fractions.

1 Express \(\frac { 3 x } { ( 2 - x ) \left( 4 + x ^ { 2 } \right) }\) in partial fractions.

1 Express \(\frac { 5 x } { ( x - 1 ) \left( x ^ { 2 } + 4 \right) }\) in partial fractions.

5. Express \(\frac { 5 x ^ { 2 } + x + 12 } { x ^ { 3 } + 4 x }\) in partial fractions.
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4 Express \(\frac { 5 x ^ { 2 } + x + 12 } { x ^ { 3 } + 4 x }\) in partial fractions.

3 Express \(\frac { x + 6 } { x \left( x ^ { 2 } + 2 \right) }\) in partial fractions.