# Worksheet: Partial Fractions: Repeated Linear Factors

In this worksheet, we will practice decomposing rational expressions into partial fractions when the denominator has repeated linear factors.

**Q1: **

Consider the rational expression . The following strategy reveals it as a sum of partial fractions.

What is the value of when ? Let us call this .

So, . What is ? Give the factored and simplified form.

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Repeat the first step with and to find and so that . What, finally, is the partial fraction decomposition of ?

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**Q5: **

When the expression is expressed as a sum of partial fractions, what form will it take?

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**Q6: **

Determine the partial fraction decomposition of .

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