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Section 5.5 : Partial Fractions

Determine the partial fraction decomposition of each of the following expressions.

1. \( \displaystyle \frac{{17x - 53}}{{{x^2} - 2x - 15}}\) Solution
2. \( \displaystyle \frac{{34 - 12x}}{{3{x^2} - 10x - 8}}\) Solution
3. \( \displaystyle \frac{{125 + 4x - 9{x^2}}}{{\left( {x - 1} \right)\left( {x + 3} \right)\left( {x + 4} \right)}}\) Solution
4. \( \displaystyle \frac{{10x + 35}}{{{{\left( {x + 4} \right)}^2}}}\) Solution
5. \( \displaystyle \frac{{6x + 5}}{{{{\left( {2x - 1} \right)}^2}}}\) Solution
6. \( \displaystyle \frac{{7{x^2} - 17x + 38}}{{\left( {x + 6} \right){{\left( {x - 1} \right)}^2}}}\) Solution
7. \( \displaystyle \frac{{4{x^2} - 22x + 7}}{{\left( {2x + 3} \right){{\left( {x - 2} \right)}^2}}}\) Solution
8. \( \displaystyle \frac{{3{x^2} + 7x + 28}}{{x\left( {{x^2} + x + 7} \right)}}\) Solution
9. \( \displaystyle \frac{{4{x^3} + 16x + 7}}{{{{\left( {{x^2} + 4} \right)}^2}}}\) Solution