Question Type 3: Doing quadratic factors and linear factors Exercises

Simplify and decompose into partial fractions: $\displaystyle \frac{x^2 -4}{x^3 - x}$.

Perform partial fraction decomposition on $\displaystyle \frac{2x^3 +5x^2 +x +3}{x^2 -4}$.

Express $\displaystyle \frac{x^2 +1}{(x-2)^2}$ in partial fractions.

Decompose $\displaystyle \frac{3x^2 -3x +4}{(x^2+3)(x-1)}$ into partial fractions.

Express $\displaystyle \frac{3x-1}{(x+2)(x-3)}$ in partial fractions.

Decompose into partial fractions: $\displaystyle \frac{x^2 + 2x +5}{x^3 + x^2 - x -1}$.

Find the partial fraction decomposition of $\displaystyle \frac{4x+7}{x^2 + 3x +2}$.

Decompose the rational expression $\displaystyle \frac{2x+3}{x^2 - x - 2}$ into partial fractions.

Decompose $\displaystyle \frac{2x^2 +3x +4}{(x-1)(x^2+1)}$ into partial fractions.

Decompose $\displaystyle \frac{4x^2 +2x +1}{(x-3)^2(x+2)}$ into partial fractions.