Question Type 2: Applying partial fractions on linear factors on higher powers Exercises

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

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

Find the partial fraction decomposition of $\frac{5x + 7}{(x - 2)(x - 4)^2}$.

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

Perform partial fraction decomposition for $\frac{2x^2 + 3}{(x - 1)^2(x + 3)^2}$.

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

Find the partial fraction decomposition of $\frac{2x^4 - x^2 + 3}{(x - 3)(x + 1)^2}$.

Express $\frac{5x + 4}{(x - 5)^3(x + 1)^2}$ as partial fractions.

Find the partial fractions of $\frac{x^3 + 2x^2 - x + 5}{(x - 1)(x - 2)^2}$.

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