Grade 11: Partial Fraction Decomposition Worksheet
This worksheet focuses on decomposing rational expressions into simpler fractions, covering various cases of denominators for Grade 11 Algebra students.
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Partial Fraction Decomposition
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Decompose each rational expression into its partial fractions. Show all your work.
1. Decompose the following expression: $$\frac{5x - 1}{(x - 1)(x + 2)}$$
2. Decompose the following expression: $$\frac{x + 7}{x^2 - x - 6}$$
3. Decompose the following expression: $$\frac{2x + 3}{(x + 1)^2}$$
4. Decompose the following expression: $$\frac{x^2 - 3x + 4}{x(x - 2)^2}$$
5. Decompose the following expression: $$\frac{3x - 2}{x(x^2 + 1)}$$
6. Decompose the following expression: $$\frac{x^2 + 2x + 3}{(x^2 + 4)^2}$$
7. Which of the following is the correct partial fraction decomposition for $$\frac{x}{x^2 - 4}$$?
$$\frac{1}{x - 2} - \frac{1}{x + 2}$$
$$\frac{1/2}{x - 2} + \frac{1/2}{x + 2}$$
$$\frac{1}{x - 2} + \frac{1}{x + 2}$$
$$\frac{1/2}{x - 2} - \frac{1/2}{x + 2}$$
8. The expression $$\frac{x^3 + 1}{x^2 + x}$$ requires long division before partial fraction decomposition.
True
False