Partial Fraction Decomposition Worksheet
This worksheet focuses on decomposing rational expressions into simpler fractions for Grade 9 algebra students.
Includes
Standards
Topics
Partial Fraction Decomposition
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Decompose each rational expression into its partial fractions. Show all your work.
1. Partial fraction decomposition is used to rewrite a complex rational expression as a sum of simpler expressions.
2. When the denominator has distinct linear factors, the numerators of the partial fractions are constants.
3. To find the unknown constants, we can use the method of equating coefficients or the method.
1. Decompose the following expression: (x + 7) / (x^2 + x - 6)
2. Decompose the following expression: (5x - 1) / (x^2 - 1)
1. Which of the following is the correct partial fraction decomposition of 1 / (x^2 - 4)?
A/(x-2) + B/(x+2)
A/(x^2) + B/(-4)
A/(x-2)^2
(A+B)/(x^2-4)
2. When decomposing a rational expression, if the degree of the numerator is greater than or equal to the degree of the denominator, what operation should be performed first?
Factoring the numerator
Long division
Multiplying by the common denominator
Substituting values for x
1. The denominator of a rational expression must be factored completely before performing partial fraction decomposition.
True
False
2. The degree of the numerator in a proper rational expression is always greater than or equal to the degree of the denominator.
True
False
Match the type of factor with the form of its partial fraction.
1. Distinct Linear Factor (ax + b)
a. (Ax + B) / (ax^2 + bx + c)
2. Repeated Linear Factor (ax + b)^n
b. A / (ax + b)
3. Irreducible Quadratic Factor (ax^2 + bx + c)
c. A/(ax+b) + B/(ax+b)^2 + ... + N/(ax+b)^n