What is the first step in setting up partial fractions for $$\frac{2x-7}{(x-1)(x^2+2)}$$ ?

Identify the form: $$\frac{A}{(x-1)} + \frac{Bx + C}{(x^2 + 2)}$$ .

What is the first step in setting up partial fractions for $$\frac{5x+3}{x(x+4)^2}$$ ?

Identify the form: $$\frac{A}{x} + \frac{B}{(x+4)} + \frac{C}{(x+4)^2}$$ .

What is the first step in setting up partial fractions for $$\frac{3x+2}{x^2+x-6}$$ ?

Factor the denominator: $$x^2+x-6 = (x+3)(x-2)$$ and identify the form: $$\frac{A}{(x+3)} + \frac{B}{(x-2)}$$ .

What is the first step in setting up partial fractions for $$\frac{x+4}{x(x^2+2)}$$ ?

Identify the form: $$\frac{A}{x} + \frac{Bx + C}{(x^2 + 2)}$$ .

What is the first step in setting up partial fractions for $$\frac{3x}{(x+3)^2}$$ ?

Identify the form: $$\frac{A}{(x+3)} + \frac{B}{(x+3)^2}$$ .

What is the purpose of partial fraction decomposition?

To express a rational function as a sum of simpler fractions, making it easier to integrate or analyze.

What is the significance of the degree of the numerator in partial fraction decomposition?

The degree of the numerator must be less than the degree of the denominator for proper decomposition.

What is a common mistake when setting up partial fractions?

Assuming the form of the partial fractions without correctly factoring the denominator.

How can you verify your partial fraction decomposition?

By combining the fractions back into a single rational function and checking if it equals the original function.

What is the role of the constants A, B, C, etc., in partial fraction decomposition?

They are the unknown coefficients that need to be determined to match the original rational function.

Partial Fraction 1 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the general form of partial fraction decomposition for a rational function with distinct linear factors?

Back

2.

FLASHCARD QUESTION

Front

What is the general form of partial fraction decomposition for a rational function with repeated linear factors?

Back

3.

FLASHCARD QUESTION

Front

What is the general form of partial fraction decomposition for a rational function with irreducible quadratic factors?

Back

4.

FLASHCARD QUESTION

Front

What is the general form of partial fraction decomposition for a rational function with repeated irreducible quadratic factors?

Back

5.

FLASHCARD QUESTION

Front

How do you determine the coefficients in partial fraction decomposition?

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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